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