Question

Describe how to transform the quantity of the fifth root of x to the seventh power, to the third powerinto an expression with a rational exponent. Make sure you respond with complete sentences.

Answer 1

$$
\large{
\left(\left (\sqrt[5]{x}\right )^7\right)^3\\
=\left (\left (x^{1/5}\right )^7\right))^3\\
=\left(x^{7/5}\right)^3\\
=x^{\frac{7*3}{5}}\\
=x^{\frac{21}{5}}\\
}
$$

Expand the 5th root of x into an exponent with a fraction, 1/5
In the exponent of x, multiply 7 times this value
In the exponent of x, Multiply the result times 3

Answer 2

wouldnt the 7+3=10 instead of 11?

Answer 3

It's actually 7x3 which =21

Answer 4

so its x 21 over 5?

Answer 5

Yes.

x^ 21/5

Answer 6

@JTsoccer

Good question. That is a common mistake.

You are thinking about something like x^7 * x^3 = x^ (7+3) = x^(10)

However, (x^7)^3 is not the same as x^7 * x^3.

Because,
(x^7)^3 = x^7 * x^7 * x^7 = x^(7+7+7) = x^(21).

Answer 7

@pizzaqueen5