Middle School

What is the cube root of [tex]8x^{27}[/tex]?

A. [tex]2x^3[/tex]
B. [tex]2x^9[/tex]
C. [tex]4x^3[/tex]
D. [tex]4x^9[/tex]

Answer :

Answer:

2 x^9

Step-by-step explanation:

8x ^27

We want to take the cube root

(8x ^27) ^1/3

We know that (ab)^1/3 = a^1/3 * b^1/3

(8) ^ 1/3 (x ^27) ^1/3

Re writing 8 as 2^3

(2 ^3) ^ 1/3 (x ^27) ^1/3

We know that a^b^c = a^ (b*c)

(2 ^(3* 1/3) *x ^(27 *1/3)

2 ^ 1 * x ^ 9

2 x^9

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