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 option $\frac{25a^9b^{10}}{6}$ is correct

Therefore $\frac{(5ab)^3}{30a^{-6}b^{-7}}=\frac{25a^9b^{10}}{6}$

Step-by-step explanation:

Given expression can be written as $\frac{(5ab)^3}{30a^{-6}b^{-7}}$

Now to simplify the given fractional expression :

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

$=\frac{5^3a^3b^3}{30a^{-6}b^{-7}}$

$=\frac{5^3a^3b^3a^6b^7}{30}$ ( by using the property $a^m=\frac{1}{a^{-m}}$)

$=\frac{125a^3a^6b^3b^7}{30}$

$=\frac{25a^{3+6}b^{3+7}}{6}$ ( by using the property $a^m.a^n=a^{m+n}$ )

$=\frac{25a^9b^{10}}{6}$

Therefore $\frac{(5ab)^3}{30a^{-6}b^{-7}}=\frac{25a^9b^{10}}{6}$

Therefore the option $\frac{25a^9b^{10}}{6}$ is correct