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the expression, 4th square root of 7 over 3rd square root of 7, equals 7 raised to what power?

 Dec 30, 2022
 #1
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-1

The exponent is 5/8.

 Dec 30, 2022
 #2
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I solved it a different way and got a different answer:

 

So we have the 4th square root of 7 over the 3rd square root of 7 is equal to 7 raised to what power...

Let's write this as an expression, with x being the exponent of 7:

\((\sqrt[4]{7})/(\sqrt[3]{7}) = 7^x\)

We simplify:
\((7^{1/4})*(7^{-1/3}) = 7^x\)

We know when multiplying numbers with same bases, we add exponents so:

\(7^{1/4-1/3}=7^x\)

\(7^{3/12-4/12}=7^x\)

\(7^{-1/12}=7^x\)

This simplifies to:

\(x = -1/12\)

So the exponent is:

-1/12

 

(I advise you to read my work, because I could be wrong)

 Dec 30, 2022

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