Question

How to write an equivalent expression using exponents for this question: sq. root, of the sq. root of 81x^8?

Answer 1

\[\sqrt{}\sqrt{81x^{8}}\]

Answer 2

and also, \[\sqrt{}\sqrt[3]{8x ^{7}}\]

Answer 3

Do you know the answer if there was only 1 square root?

Answer 4

no, I don't.. I get so confused with the square roots..

Answer 5

\[\sqrt{stuff}= stuff^{\frac{1}{2}}\]
try doing
\[\sqrt{81 x^{8}}= ??^{\frac{1}{2}}\]

Answer 6

ohh, it's 9^1/2

Answer 7

half way... you also need (x^8)^(1/2)

Answer 8

it says 4.

Answer 9

And if you have something like\[(x^{8})^{\frac{1}{2}}= x^{8\cdot\frac{1}{2}}= x^{4}\]
multiply the exponents

Answer 10

ohhh... i see. So, after I half the base I do that?

Answer 11

when there's two square roots?

Answer 12

the answer with one square root is
\[81^{\frac{1}{2}}x^{8\cdot\frac{1}{2}}= 9x^{4}\]
so put the 9x^4 in a square root and do it again

Answer 13

I'm not sure what they want for the final answer. If you rewrite the expression using exponents (and do not simplify it) it would look like this
\[81^{\frac{1}{4}}x^{2}\]

Answer 14

Your other problem is the square root of a cube root?
a cube root is the same as using an exponent of 1/3 (instead of 1/2)

Answer 15

ohhhhh, i see. Thanks!!