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

Answer:

Option D.

Step-by-step explanation:

The given expression is

$\dfrac{(5ab)^3}{30a^{-6}b^{-7}}$

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

The given expression can be rewritten as

$\dfrac{5^3a^3b^3}{30a^{-6}b^{-7}}$     $[\because (ab)^m=a^mb^m]$

$\dfrac{125}{30}\times \dfrac{a^3}{a^{-6}}\times \dfrac{b^3}{b^{-7}}$

$\dfrac{25}{6}\times a^{3-(-6)}\times b^{3-(-7)}$    $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$\dfrac{25}{6}\times a^{3+6}\times b^{3+7}$

$\dfrac{25a^9b^{10}}{6}$

Therefore, the correct option is D.