Question

Which expression is equivalent to

Answer 1

The equivalent expression of $\frac{(5ab)^3}{30ab^{-7}}$ is $\frac{25a^{2}b^{10}}{6}$

How to determine the equivalent expression?

The expression is given as:

$\frac{(5ab)^3}{30ab^{-7}}$

Expand the numerator

$\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}$

Divide 125 and 30 by 5

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}$

Apply the law of indices

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}$

Evaluate the exponent

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}$

Hence, the equivalent expression of $\frac{(5ab)^3}{30ab^{-7}}$ is $\frac{25a^{2}b^{10}}{6}$

Read more about equivalent expression at:

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