Question

Simplify.

(-3ab^3)^4

A. -7ab^12
B. -12a^4b^7
C. -81a^4b^7
D. 81a^4b^12

Answer 1

D

Explanation:

Use main properties of powers:

1.
`(a\cdot b)^m=a^m\cdot b^m;`

2.
`(a^m)^n=a^(mn).`

Thus,

`(-3ab^3)^4=(-3)^4\cdot a^4\cdot (b^3)^4.`

Hence,

`(-3)^4=81,\\ \\(b^3)^4=b^(3\cdot 4)=b^(12),`

then

`(-3ab^3)^4=(-3)^4\cdot a^4\cdot (b^3)^4=81a^4b^(12).`