Question

Which expression is equivalent to StartFraction (5 a b) cubed Over 30 a Superscript negative 6 Baseline b Superscript negative 7 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.

StartFraction a Superscript 7 Baseline b Superscript 10 Baseline Over 6 EndFraction
StartFraction 125 a Superscript 18 Baseline b Superscript 21 Baseline Over 30 EndFraction
StartFraction 25 a cubed b Superscript 4 Baseline Over 6 EndFraction
StartFraction 25 a Superscript 9 Baseline b Superscript 10 Baseline Over 6 EndFraction

Answer 1

The correct option is D

Explanation:

Answer 2

Option D.

Explanation:

The given expression is

`((5ab)^3)/(30a^(-6)b^(-7))`

We need to find the expression, which is equivalent to the given expression.

The given expression can be rewritten as

`(5^3a^3b^3)/(30a^(-6)b^(-7))`
`[\because (ab)^m=a^mb^m]`

`(125)/(30)* (a^3)/(a^(-6))* (b^3)/(b^(-7))`

`(25)/(6)* a^(3-(-6))* b^(3-(-7))`
`[\because (a^m)/(a^n)=a^(m-n)]`

`(25)/(6)* a^(3+6)* b^(3+7)`

`(25a^9b^(10))/(6)`

Therefore, the correct option is D.