Question

Consider the expression. (x^3y^-2/2^2x^-5y^3)^3. What is the result of applying the quotient of powers rule to the expression?

Answer 1

on e2020 i got the answer

C

1x^8

( ____ ) ^3

2^2y^5

Answer 2

`(x^(24) )/(8y^(15))`

Explanation:

`((x^(3)y^(-2))/(2x^(-5)y^(3)))^3`

We will use

1)Product Rule

a^m ∙ a^n = a^(m + n),

this says that to multiply two exponents with the same base, you keep the base and add the powers.

2)Quotient Rule

`(a^(m) )/(a^(n))=a^(m-n)`

this says that to divide two exponents with the same base, you keep the base and subtract the powers.

So by considering these two laws

`(x^(3-(-5))y^(-2-3)})/2 )^(3)`

`((x^(8)y^(-5) )/(2))^(3)`

`((x^(8) )/(2y^(5)))^(3)`

3)Power Rule (Powers to Powers)

(a^m)^n = a^(mn)

`(x^(24) )/(8y^(15))`