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# Yep, plz help

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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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The exponent is 5/8.

Dec 30, 2022
#2
+105
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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