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## Class 8 Math (Assamese)

### Course: Class 8 Math (Assamese)>Unit 11

Lesson 2: Negative exponents

# Negative exponents

Negative exponents can be rewritten in two ways. Firstly, start with 1 and divide it by 2 the same number of times as the exponent. Secondly, take the reciprocal of the base and raise it to the positive exponent. Created by Sal Khan.

## Want to join the conversation?

• i'm confused. so at he says that 1/25/64 is just going to be 64/25 but never explained why? How did he reach that conclusion? i'm so lost!
• I assume it is 1/(25/64), and to divide fractions, you reciprocate (flip) the one in the denominator and multiply, so 1 * 64/25 = 64/25. If it were (1/25)/64, then that would be a different answer 1/25 * 1/64.
• I'm confused. If for example 2^4 is 2*2*2*2=16, why is 2^-4 meaning 2/2/2/2 equal to 1/4 rather than 1/16?
• Negative exponents move the value to the other side of a division sign, so 2^-4/1 makes it 1/2^4. Exponents are a shortcut for multiplication, not division.
• It's just to clarify that there is a 1. Say we have `3^2 = 9`; `3^1 = 3`; `3^0 = ?`. What would 3^0 be? We know it's 1 and since there are no 3's to multiply 1 with, then we say it's 1. Once you understand the concept, you don't need to write it at all!
• An exponent says how many times to use the base in multiplication. So for example, 2^2 = 2 x 2 = 4.

3^5 = 3 x 3 x 3 x 3 x 3 = 243

Intuitively thinking based on the above: 2^-2:

How does a negative exponent become a reciprocal? That doesn't make sense to me yet.
• It's based on exponent rules. 3^2 x 3^3 would be (3 x 3) x (3 x 3 x 3), or 3^5. So for multiplication of two exponents with the same bases, you add the exponents. What about division? 3^3 / 3^2 is (3 x 3 x 3) / (3 x 3), so it would be 3/1, or 3, which is 3^1. So for division with the same base, you subtract the exponent. If you have 3^3 / 3^3, you would have 3^(3-3) = 3^0 because of this rule, so 3^0 = 3^3/3^3, which turns out to be 1. Anything to the 0th power is 1. if you take 3^0 / 3^1, you have 3^-1, which is also 1/3, so it's the reciprocal. I hope this makes sense to you.
• I think a negative exponent is basically the reciprocal of the positive reciprocal. Is this right?
• Slightly yes but better understand that if the power is minus it has to change its place from nominator to denominator or denominator to nominator
AND when it changes its place the minus become positive
• "1 over 25/64 is just going to be 64/25".

Why?

Please explain this in detail (or provide a link to a lesson on this). I do not understand.
• To solve for "1 over 25/64" order of operation says to divide 25/64 first, to get 0.390625. Then, you divide 1/0.390625, you get 2.56. If you try to divide 64/25, you will see that it equals 2.56. In other words: "1 over 25/64" is equal to 64/25. Hope this helps :)
• Is there any other way to understand 2 to the power of -4 and, what this negative symbol does?
• The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base.

So 2^(-4) = 1/(2^4) = 1/(2*2*2*2) = 1/16. The answer is 1/16.

Have a blessed, wonderful New Year!
• I've always been so confused on negative exponents, this helped me a lot!
But I don't understand how 1/(25/64)=64/25?
• I asked chatgpt about it and this is the answer it returned. This helped me a lot!

(this is just the excerpt that helped me)
Now, let's consider a fraction like a/b, where "a" is the numerator and "b" is the denominator. Dividing by this fraction means we are asking how many times a fraction with value (a/b) fits into the dividend.

Let's use the dividend "1" for our example: 1 / (a/b).

To determine how many times the fraction (a/b) fits into 1, we can rephrase the question as "what number, when multiplied by (a/b), gives us 1?" In other words, we want to find the multiplicative inverse of (a/b) that, when multiplied, yields 1.

The multiplicative inverse of a fraction a/b is its reciprocal, which is b/a. Why? Because when you multiply a fraction by its reciprocal, the result is always 1.
• REALLY CONFUSED! Ok i don't get how you calculate 2^-4 how do you do that. It makes no sense to me?
• 2^-4. Okay, I'll give an example.
When the number has a negative exponent, you put that number at the denominator. For example, 1^-1 will be 1/1^1. The exponent is now positive because it was moved down to the denominator. Same thing if there is a negative power on the bottom of the fraction. 1/2^-2 is 4. 2^2 is 4, but the power is negative so I had to move it to the top.
So 2^-4 will be 1/16, because 2^4 is 16, and it's negative and it's on the top, so I move it down.
Hope this helped!