Question

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

Answer 1

can you check my work

Answer 2

x/a^n=x 20/3

Answer 3

do i simplify the radical next

Answer 4

if you mean
\[ \left( \sqrt[3]{x^4}\right)^5 = x^\frac{20}{3} \]
yes, that is correct.

I don't know what a^n means in
x/a^n=x 20/3

Answer 5

idk how to type the square root on my laptop

Answer 6

but yes thats what i have on my paper

Answer 7

the "cube root" of x^4 can be written as
\[ \left(x^4\right)^\frac{1}{3} \]
and we can re-write that by "multiplying the exponents"
to get
\[ x^\frac{4}{3} \]
and if we raise that to the 5th power
\[ \left(x^\frac{4}{3} \right)^5 \]
we multiply by expoents again to simplify to the answer

Answer 8

is that x^3

Answer 9

are you asking about
\[ \left(x^\frac{4}{3} \right)^5 \]?
to simplify to just one expoent , figure out 5* 4/3

Answer 10

20/3

Answer 11

yes, so x^(20/3) is another way to write
\[ \left( \sqrt[3]{x^4}\right)^5 \]

Answer 12

so these are the steps

Answer 13

yes, the first step is to replace the cube root "sign" with an exponent of 1/3
see the post a few steps up.