Question

How do you simplify `(- 3x ^ { - 4} y z ^ { - 7} ) ^ { 2} ( 4x y ^ { 5} z ^ { - 2} z ^ { - 2} ) ^ { 3}`?

Answer 1

`(-3x^(-4)yz^(-7))^2(4xy^5z^(-2)z^(-2))^3=color(blue)((576y^17)/(x^5z^26)`

Explanation:

Simplify:

`(-3x^(-4)yz^(-7))^2(4xy^5z^(-2)z^(-2))^3`

Apply power rule: `(a^m)^n=a^(m*n)`

`(-3^2x^(-4*2)y^(1*2)z^(-7*2))(4^3x^(1*3)y^(5*3)z^(-2*3)z^(-2*3))`

Simplify.

`9x^(-8)y^2z^(-14)64x^3y^(15)z^(-6)z^(-6)`

Collect like terms.

`9xx64x^(-8)x^3y^2y^(15)z^(-14)z^(-6)z^(-6)`

Simplify `9xx64` to `576`.

`576x^(-8)x^3y^2y^(15)z^(-14)z^(-6)z^(-6)`

Apply product rule: `a^ma^n=a^(m+n)`

`576x^(-8+3)y^(2+15)z^(-14+(-6)+(-6))`

Simplify.

`576x^(-5)y^(17)z^(-26)`

Apply negative exponent rule: `a^(-m)=1/a^m`

`(576y^17)/(x^5z^26)`