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

$\frac{-8}{27}a^{15}$

Answer 1

Answer:

A.

$(4x^3)^3$

C.

$(-0.2b^2)^3$

D.

$\left(-\dfrac{2}{3}a^5\right)^3$

Step-by-step 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 $-\frac{8}{27}a^{15}.$

Note that

$-\dfrac{8}{27}=-\dfrac{2^3}{3^3}=\left(-\dfrac{2}{3}\right)^3\\ \\a^{15}=(a^5)^3,$

then

$-\dfrac{8}{27}a^{15}=\left(-\dfrac{2}{3}\right)^3\cdot (a^5)^3=\left(-\dfrac{2}{3}a^5\right)^3$