How do you simplify (x ^ { 5} y ^ { - 9} ) ^ { 3}?

2 Answers
Mar 3, 2018

Since the expression is inside parenthesis, the exponent 3 will affect the entire expression

Explanation:

In this form, the laws of exponents tell us (a^xb^y)^n)=a^{nx}b^{ny}

So, in your case (x^5y^{-9})^3 -> x^{5*3}y^{-9*3}->x^15y^-27

Mar 3, 2018

x^15*y^(-27)

Explanation:

color(red)((1)(M*N)^Z=M^Z*N^Z)
color(red)((2)(A^M)^N=A^(MN))
Here,
(x^5*y^(-9))^3=(x^5)^3*(y^(-9))^3, [Applying (1)]
(x^5*y^(-9))^3=(x^((5)(3))*(y^((-9)(3))), [Applying (2)]
(x^5*y^(-9))^3=x^15*y^(-27)