Respuesta :
ANSWER
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{9} b^{10} }{6} [/tex]
EXPLANATION
To find the expression that is equivalent to
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
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,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 5^{3}a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
This gives us,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 125a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
We simplify by applying the following law of exponent,
[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]
Our expression now becomes,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 - - 6} b^{3 - - 7} }{6} [/tex]
We simplify further to get,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 + 6} b^{3 + 7} }{6} [/tex]
This finally gives us,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{9} b^{10} }{6} [/tex]
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{9} b^{10} }{6} [/tex]
EXPLANATION
To find the expression that is equivalent to
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
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,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 5^{3}a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
This gives us,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 125a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} } [/tex]
We simplify by applying the following law of exponent,
[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]
Our expression now becomes,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 - - 6} b^{3 - - 7} }{6} [/tex]
We simplify further to get,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 + 6} b^{3 + 7} }{6} [/tex]
This finally gives us,
[tex] \frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{9} b^{10} }{6} [/tex]
Answer:
Step-by-step explanation:
Alright, lets get stared.
The given expression as:
[tex]\frac{(5ab)^3}{30a^{-6} b^{-7} }[/tex]
[tex]\frac{5^3a^3b^3}{30a^{-6} b^{-7}}[/tex]
[tex]\frac{125a^3b^3}{30a^{-6} b^{-7}}[/tex]
[tex]\frac{125a^3b^3}{30}*a^6b^7[/tex]
[tex]\frac{125a^{3+6} b^{3+7} }{30}[/tex]
[tex]\frac{125a^9b^{10} }{30}[/tex]
125 and 30 can be simplified, so
[tex]\frac{25a^9b^{10} }{6}[/tex]
Hence the answer is [tex]\frac{25a^9b^{10} }{6}[/tex] : Answer
Hope it will help :)
