Question

Which expression is equivalent to (5ab)^3/30a^-6b^-7

Answer 1

Answer:

Step-by-step explanation:

Alright, lets get stared.

The given expression as:

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

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

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

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

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

$\frac{125a^9b^{10} }{30}$

125 and 30 can be simplified, so

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

Hence the answer is $\frac{25a^9b^{10} }{6}$   :    Answer

Hope it will help :)

Answer 2

ANSWER


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



EXPLANATION

To find the expression that is equivalent to
$\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} }$

we must simplify it.


We apply the laws of exponents in the simplification.



First, let us share the cubic exponent for each factor in the numerator to obtain,


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


This gives us,


$\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 125a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} }$


We simplify by applying the following law of exponent,


$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$


Our expression now becomes,



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



We simplify further to get,


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




This finally gives us,


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