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. type "numerator" or "denominator" to complete each statement.

a) Numerator
b) Denominator
c) Both
d) None

Answer 1

To simplify the expression [(x^2y^3)^-1(x^-2y^2z)^2]^2, first apply the power rule and simplify each term. The numerator is y^7z^8 and the denominator is 1.

Step-by-step explanation:

To simplify the given expression [(x2y3)-1(x-2y2z)2]2, we first apply the power rule, which states that raising an exponential expression to another exponent is equivalent to multiplying the exponents. So, we have:

(x2)-1(x-2)2y32y22z22

Next, we can simplify each term:

x-2 multiplied by x2 gives us x-2+2, which is equal to x0 or 1.

y32 multiplied by y22 gives us y3+4, which is equal to y7.

z22 multiplied by z22 gives us z4+4, which is equal to z8.

Therefore, the simplified expression is 1 y7 z8. Now, let's complete the statements: The numerator is y7 z8 and the denominator is 1.