If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 3: Powers of fractions and decimals

# Powers of fractions

Raising fractions to a power is a fundamental math skill. To do this, simply multiply the numerators and denominators separately. For example, when raising a fraction like 2/3 to the third power, multiply the numerators (2 × 2 × 2 = 8) and the denominators (3 × 3 × 3 = 27) to get the result 8/27. This method applies to all powers, making it easy to understand and apply. Created by Sal Khan.

## Want to join the conversation?

• hello I tried typing 2/3^2 in a calculator and I got a different answer than 8/27 how come
• This is because of the order of operations. by typing 2/3^2, you told the calculator to calculate 2 divided by 3 to the power of 2, rather that 2/3 to the power of 2. The order of operations makes it that you calculate exponents before division. To get the right answer, you should input: (2/3)^2. Also (2/3)^2 is 4/9, not 8/27. That is (2/3)^3. Hope this helps.
• where is the 1 coming from
• I still don't get where the 1 is coming from. Why do you put it? I understand that one means a whole but still why do you decide to put 1? Thanks!
(1 vote)
• Why are there parenthesis surrounding the fraction? If you follow the order of operations PEMDAS, would you not treat the fraction as a division problem and do it first, then the exponent? In the example above, shouldn't it be written 2/3 cubed instead of (2/3) cubed?
• PEMDAS - The E = Exponents. They come before D = Division.
If you write 2/3 cubed (with the exponent 3 in superscript beside the fraction, the exponent would be on the 2 and you would end up with (2*2*2)/3 = 8/3

If you write 2/3 cubed with the exponent in superscript beside the 3, you end up with 2/(3*3*3) = 2/27

If you want to cube the entire fraction, the parentheses are required. (2/3)^3 = (2/3)(2/3)(2/30 = 8/27

Hope this helps.
• So the fast way is,
Numerator^exponent
Denominator^exponent

Place the answer in the orignal form.
• Why is 0.2 Times 0.2 = 0.04 and not 0.4?
• Because when you Do decimal times decimal you add the amount of places each decimal had to go to get to the right
• Ok I want to know how the barnacles you got 2 x2x2 is 8 plz tell me I think you got it wrong and I want you to tell straight up that’s right or wrong because if 2x2x2 is 6 so plz don’t give us missed information
(1 vote)
• 2x2x2 equals 8,and if I break it down
2x2 = 4
4x2 = 8
I see the confusion, but 2 to the power of 3 is 2 times itself 3 times, rather than just 2 x 3
• How would multiply a mixed fraction by an exponent?
(1 vote)
• 1. Convert the mixed fraction to an improper fraction, if it's not already in that form. To convert a mixed fraction to an improper fraction, multiply the whole number part by the denominator and add the numerator. Place the result over the denominator.
2. Apply the exponent to the numerator or the entire fraction, depending on the specific exponent rule or instruction.
3. Simplify the fraction, if possible, by finding common factors between the numerator and denominator.
• hello l tried typing 2/3^2 in a calculator and l got a different answer than 8/27 how come?
(1 vote)
• Do you mean 2/3^3?
If you typed it into the calculator as 2/3^3 the calculator will follow the order of operations so it will only cube the 3, if you want to cube the whole fraction you have to put parenthesis around the fraction like (2/3)^3 so that it will cube the whole thing.