Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.

Question

(x^-2y)^2 (5x^0y)^3

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(4x^3y^4)^3 (xy^-1)^3

Answer 1

Breaking this down a little, we can simplify each part like this:

(x^-2y)² = x^-4y² = y²/x⁴

(5x⁰y)³ = 5³x⁰y³ = 125(1)(y³) = 125y³

(4x³y⁴)³ = 4³x⁹y¹² = 64x⁹y¹²

(xy^-1)³ = x³y^-3 = x²/y³

Now, we can multiply the top two: (y²/x⁴)(125y³) = 125y⁵/x⁴

And multiply the bottom two: (64x⁹y¹²)(x²/y³) = 64x¹¹y⁹

Then divide those to get: (125y⁵/x⁴)/(64x¹¹y⁹). This is like dividing fractions because the top expression is rational. So keep the top (125y⁵/x⁴), switch it to multiplication, and flip the bottom (1/64x¹¹y⁹) which becomes: