who added letters in math i would like to have a conversation with them please

François Viète is the person you should speak to about adding numbers to math. At the end of the 16th century, François Viète introduced the idea of representing known and unknown numbers by letters, nowadays called variables, and the idea of computing with them as if they were numbers—in order to obtain the result by a simple replacement.

I'm confused by the fact that all exponents to the 0th power equals 1. Why is this? Shouldn't the answer be zero instead?

When you look at it, not really. Let's pick a small number: 2 2 to the power of 4=16 2 to the power of 3=8 2 to the power of 2=4 2 to the power of 1=2 Now when you look at these numbers, you should notice a pattern. 8/2=4, and 4/2=2. Now 2 divided by 2 would give us the answer to 2 to the power of 0, which is equal to 1. Hope that you understand now. Good luck!!

What's 0 to the 0th power ?

Well it will be undefined. See this case 2^3=2*2*2 =8 2^2=2*2 =4 2^1=2 =2 2^0=1 The reason we get 2^0 is because for every 2^{n-1}, we are dividing the 2^n by 2, for example to get value of 2^0, we are dividing the 2^1=2 by the 2. The result is therefor 1. But in case of 0, we will be dividing the 0 by the 0. Because 0^1=0 and then we will be diving by our base (which is 0), the result will be 0/0, which is undefined. I hope you got my point. Have a nice day.

i wish we can go back to 1+1 and 2+2

If you still using them don’t worry but to survive in this digital era and going to Mars you will need those more complicated mathematical expressions and equations to solve your everyday problems and you may solve one of the world problems one day you never know. My humble advice to anyone who is taking mathematics is to start from beginning and build up at your own pace so you can perceive it better and have as many examples as possible also research what you can't understand and try to solve as many problems as you can

Can an exponent have an exponent?

Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.

can an exponent have an exponent

Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.

Is there an answer to x^3 without "x" being part of the answer?

The only way you can get an answer for x^3 without have "x" be part of the answer is if you know the value of "x". For example, if someone says x=4, then we can find x^3. x^3 = 4^3 = 64. Otherwise, you are stuck with the "x".

Why do we have to learn all of this??

You never know when this might come up in life. Sometimes, it forms the border between getting accepted into your college, or getting a good grade on a test. Wish you luck on whatever you're learning!

Main content

Algebra basics

Course: Algebra basics > Unit 6

Lesson 1: Exponent properties intro

Exponent properties review

Google Classroom

Review the common properties of exponents that allow us to rewrite powers in different ways. For example, x²⋅x³ can be written as x⁵.

Property	Example
$x^{n} \cdot x^{m} = x^{n + m}$ ‍	$2^{3} \cdot 2^{5} = 2^{8}$ ‍
$\frac{x^{n}}{x^{m}} = x^{n - m}$ ‍	$\frac{3^{8}}{3^{2}} = 3^{6}$ ‍
${(x^{n})}^{m} = x^{n \cdot m}$ ‍	${(5^{4})}^{3} = 5^{12}$ ‍
$(x \cdot y)^{n} = x^{n} \cdot y^{n}$ ‍	$(3 \cdot 5)^{7} = 3^{7} \cdot 5^{7}$ ‍
${(\frac{x}{y})}^{n} = \frac{x^{n}}{y^{n}}$ ‍	${(\frac{2}{3})}^{5} = \frac{2^{5}}{3^{5}}$ ‍

Want to try more problems like these? Check out this exercise.

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janana
Posted 7 years ago. Direct link to janana's post “I'm confused by the fact ...”
I'm confused by the fact that all exponents to the 0th power equals 1. Why is this? Shouldn't the answer be zero instead?
Button navigates to signup pageComment on janana's post “I'm confused by the fact ...”
(30 votes)
Answer
- Hosannah H
  Posted 7 years ago. Direct link to Hosannah H's post “When you look at it, not ...”
  When you look at it, not really. Let's pick a small number: 2
  2 to the power of 4=16
  2 to the power of 3=8
  2 to the power of 2=4
  2 to the power of 1=2
  Now when you look at these numbers, you should notice a pattern. 8/2=4, and 4/2=2. Now 2 divided by 2 would give us the answer to 2 to the power of 0, which is equal to 1.
  
  Hope that you understand now. Good luck!!
  Comment on Hosannah H's post “When you look at it, not ...”
  (157 votes)
25jevel289
Posted 3 years ago. Direct link to 25jevel289's post “who added letters in math...”
who added letters in math i would like to have a conversation with them please
Button navigates to signup pageComment on 25jevel289's post “who added letters in math...”
(42 votes)
Answer
- Mikeala
  Posted 9 months ago. Direct link to Mikeala's post “François Viète is the per...”
  François Viète is the person you should speak to about adding numbers to math.
  At the end of the 16th century, François Viète introduced the idea of representing known and unknown numbers by letters, nowadays called variables, and the idea of computing with them as if they were numbers—in order to obtain the result by a simple replacement.
  Comment on Mikeala's post “François Viète is the per...”
  (14 votes)
Gabriel Zubovsky
Posted 5 years ago. Direct link to Gabriel Zubovsky's post “What's 0 to the 0th power...”
What's 0 to the 0th power ?
Button navigates to signup pageComment on Gabriel Zubovsky's post “What's 0 to the 0th power...”
(27 votes)
Answer
- Lovish Garg
  Posted 2 years ago. Direct link to Lovish Garg's post “Well it will be undefined...”
  Well it will be undefined. See this case
  2^3=2*2*2 =8
  2^2=2*2 =4
  2^1=2 =2
  2^0=1
  The reason we get 2^0 is because for every 2^{n-1}, we are dividing the 2^n by 2, for example to get value of 2^0, we are dividing the 2^1=2 by the 2. The result is therefor 1.
  
  But in case of 0, we will be dividing the 0 by the 0. Because 0^1=0 and then we will be diving by our base (which is 0), the result will be 0/0, which is undefined.
  I hope you got my point.
  Have a nice day.
  Comment on Lovish Garg's post “Well it will be undefined...”
  (27 votes)
Victoria563
Posted 4 years ago. Direct link to Victoria563's post “Can an exponent have an e...”
Can an exponent have an exponent?
Button navigates to signup pageComment on Victoria563's post “Can an exponent have an e...”
(20 votes)
Answer
- THE BETTER WINCHESTER
  Posted 2 years ago. Direct link to THE BETTER WINCHESTER's post “Of course! It's mostly se...”
  Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.
  Comment on THE BETTER WINCHESTER's post “Of course! It's mostly se...”
  (22 votes)
izayah
Posted a year ago. Direct link to izayah's post “i wish we can go back to ...”
i wish we can go back to 1+1 and 2+2
Button navigates to signup pageComment on izayah's post “i wish we can go back to ...”
(25 votes)
Answer
- RAIDA YESSIN
  Posted 9 months ago. Direct link to RAIDA YESSIN's post “If you still using them d...”
  If you still using them don’t worry but to survive in this digital era and going to Mars you will need those more complicated mathematical expressions and equations to solve your everyday problems and you may solve one of the world problems one day you never know. My humble advice to anyone who is taking mathematics is to start from beginning and build up at your own pace so you can perceive it better and have as many examples as possible also research what you can't understand and try to solve as many problems as you can
  Button navigates to signup page
  (5 votes)
kabeeralimuhammad11
Posted 7 months ago. Direct link to kabeeralimuhammad11's post “I am using Khan Academy f...”
I am using Khan Academy first time. Khan Academy teaches very Amazingly.
Button navigates to signup pageButton navigates to signup page
(25 votes)
Answer
hyost
Posted 5 months ago. Direct link to hyost's post “this is way to easy! I ha...”
this is way to easy! I have alr learned this and my mamma is making me do this :(
Button navigates to signup pageComment on hyost's post “this is way to easy! I ha...”
(16 votes)
Answer
- pringsky000
  Posted a month ago. Direct link to pringsky000's post “L couldn't be me”
  L couldn't be me
  Button navigates to signup page
  (0 votes)
TheJester(lauren)
Posted 7 months ago. Direct link to TheJester(lauren)'s post “Why do we have to learn a...”
Why do we have to learn all of this??
Button navigates to signup pageComment on TheJester(lauren)'s post “Why do we have to learn a...”
(4 votes)
Answer
- Jasmine K
  Posted 7 months ago. Direct link to Jasmine K's post “You never know when this ...”
  You never know when this might come up in life. Sometimes, it forms the border between getting accepted into your college, or getting a good grade on a test.
  
  Wish you luck on whatever you're learning!
  Button navigates to signup page
  (13 votes)
dsnider
Posted 7 years ago. Direct link to dsnider's post “Is there an answer to x^3...”
Is there an answer to x^3 without "x" being part of the answer?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kim Seidel
  Posted 7 years ago. Direct link to Kim Seidel's post “The only way you can get ...”
  The only way you can get an answer for x^3 without have "x" be part of the answer is if you know the value of "x". For example, if someone says x=4, then we can find x^3.
  x^3 = 4^3 = 64. Otherwise, you are stuck with the "x".
  Comment on Kim Seidel's post “The only way you can get ...”
  (14 votes)
Montilla, Andrea
Posted 4 years ago. Direct link to Montilla, Andrea's post “can an exponent have an e...”
can an exponent have an exponent
Button navigates to signup pageComment on Montilla, Andrea's post “can an exponent have an e...”
(6 votes)
Answer
- 50024
  Posted 2 years ago. Direct link to 50024's post “Of course! It's mostly se...”
  Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.
  Comment on 50024's post “Of course! It's mostly se...”
  (5 votes)