Question

Please help!!!!!!!!!!!!!!!!!!!!

Write the expression as a cube of a monomial.

a

64x^9




Write the expression as a cube of a monomial.

c

–0.008b^6





Write the expression as a cube of a monomial.

d


`(-8)/(27)a^(15)`

Answer 1

A.

`(4x^3)^3`

C.

`(-0.2b^2)^3`

D.

`\left(-(2)/(3)a^5\right)^3`

Explanation:

A. Given
`64x^9.`

Note that

`64=4^3\\ \\x^9=(x^3)^3,`

then

`64x^9=4^3\cdot (x^3)^3=(4x^3)^3`

C. Given
`-0.008b^6.`

Note that

`-0.008=(-0.2)^3\\ \\b^6=(b^2)^3,`

then

`-0.008b^6=(-0.2)^3\cdot (b^2)^3=(-0.2b^2)^3`

D. Given
`-(8)/(27)a^(15).`

Note that

`-(8)/(27)=-(2^3)/(3^3)=\left(-(2)/(3)\right)^3\\ \\a^(15)=(a^5)^3,`

then

`-(8)/(27)a^(15)=\left(-(2)/(3)\right)^3\cdot (a^5)^3=\left(-(2)/(3)a^5\right)^3`