Question

Write the expression by using rational exponents.

Answer 1

\[\sqrt[5]{9^{10}}\]

Answer 2

I believe it is 81.

Answer 3

yeah, thats the result. but what about the expression. that confuses me.

Answer 4

I think you follow this rule:

Rational Exponent Property.
Fractional powers, or where a number is raised to a fraction, can be converted to a radical. The numerator becomes the exponent, and the denominator becomes the index of the radical.
\[x ^{\frac{ 1 }{ n }}=\sqrt[n]{x}\]\[x ^{\frac{ m }{ n }}=\sqrt[n]{x ^{m}}\]\[x \neq0\]
Okay, let's do yours now:

Answer 5

Okay, let's do yours now:
\[\sqrt[5]{9^{10}}=9^{\frac{ 10 }{ 5 }}=9^{2}=81\]

Answer 6

Remember to write the Rational Exponent Property in your notes! It'll come in handy! ^_^

Answer 7

Awesome! Thanks! I have a couple more, can you just check my answers?

Answer 8

I'll see if I can help you. (^_^ ;)

Answer 9

\[\sqrt{8^3}\]

is it \[16\sqrt{2}\] ??

Answer 10

Yes. :3

Answer 11

is it √5 ??

Answer 12

is it 3?

Answer 13

The first one you are wrong.\[(\sqrt[6]{5})^{3}=5\frac{ 1 }{ 2 }\]and for the second one you are correct. :)

Answer 14

Awesome! that's all I needed! Thank you!

Answer 15

You are welcome. :3