Question

Which of the following represents eighth root of x to the fifth power in exponential form?

5x8

8x5

x to the five eighths power

x to the eight fifths power

Answer 1

\[\sqrt[8]{x^5} \]

A: \[5x^8 \]
B: \[8x^5 \]
C: \[x ^{5/8} \]
D: \[x ^{8/5}\]

Answer 2

I have no clue

Answer 3

explain?

Answer 4

when you see "root" as in eighth root
think "exponent is 1/ 8"

so eight root of x can be written as
\[ \sqrt[8]{x} = x^\frac{1}{8} \]

to raise it to the 5th power i.e. exponent = 5 write
\[ \left(x^\frac{1}{8} \right)^5 \]

use the rule
\[ \left(a^b\right)^c = a^{bc} \]
to simplify to
\[ x^\frac{5}{8} \]

Answer 5

so 3 things to know:

"nth root" means EXPONENT 1/n
raise to the power m means EXPONENT m
and the rule
\[ \left(a^\frac{1}{n}\right)^m = a^{\frac{1}{n}\cdot m}= a^\frac{m}{n} \]

Answer 6

Thanks