Question

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

Answer 1

Explanation:

Alright, lets get stared.

The given expression as:

`((5ab)^3)/(30a^(-6) b^(-7) )`

`(5^3a^3b^3)/(30a^(-6) b^(-7))`

`(125a^3b^3)/(30a^(-6) b^(-7))`

`(125a^3b^3)/(30)*a^6b^7`

`(125a^(3+6) b^(3+7) )/(30)`

`(125a^9b^(10) )/(30)`

125 and 30 can be simplified, so

`(25a^9b^(10) )/(6)`

Hence the answer is
`(25a^9b^(10) )/(6)` : Answer

Hope it will help :)

Answer 2

ANSWER



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



We simplify further to get,



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




This finally gives us,



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