Question

Simplify the given expression, using only positive exponents. Then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2 , x ≠ 0, y ≠ 0, z ≠ 0. The exponent on x is . The exponent on y is . The exponent on z is .

Answer 1

x=4

y=14

z=4

the guy in the comments is correct

Answer 2

Answer: y²z⁴ / x¹²

• The exponent of x is 12

• The exponent of y is 2

• The exponent of z is 4

Explanation:

1) Given expression to simplify:

$((x^2y^3)^{-1}(x^{-2}y^2z)^2)^2$

2) Property: power of power:

$(x^{-4}y^{-6})(x^{-8}y^8z^4)$

3) Property: product of powers with the same base

$x^{(-2-8)}y^{(-6+8)}z^4$

4) Add the exponents

$x^{-12}y^2z^4$

5) Pass the negative power to the denominator:

$\frac{y^2z^4}{x^{12}}$

The exponent on x is  12. The exponent on y is 2. The exponent on z is 4.