Question

Please someone answer this please

Answer 1

Option C:

`(3 a^(2) b^(11))/(2 )` is equivalent to the given expression.

Solution:

Given expression:

`$(-18 a^(-2) b^(5))/(-12 a^(-4) b^(-6))`

To find which expression is equivalent to the given expression.

`$(-18 a^(-2) b^(5))/(-12 a^(-4) b^(-6))`

Using exponent rule:
`(1)/(a^m)=a^(-m), \ \ (1)/(a^(-m))=a^(m)`

`$=(-18 a^(-2) b^(5)a^(4) b^(6))/(-12 )`

`$=(-18 a^(-2) a^(4) b^(5) b^(6))/(-12 )`

Using exponent rule:
`{a^m}\cdot{a^n}=a^(m+n)`

`$=(-18 a^((-2+4)) b^((5+6)))/(-12 )`

`$=(-18 a^(2) b^(11))/(-12 )`

Divide both numerator and denominator by the common factor –6.

`$=(3 a^(2) b^(11))/(2 )`

`$(-18 a^(-2) b^(5))/(-12 a^(-4) b^(-6))=(3 a^(2) b^(11))/(2 )`

Therefore,
`(3 a^(2) b^(11))/(2 )` is equivalent to the given expression.

Hence Option C is the correct answer.