Question

Please help and show work!

Answer 1

Step 1. Use Multiplication Distributive Property

-3 * 2^4x^4(4x^5y)^2

Step 2. Simplify 2^4 to 16

-3 * 16x^4(4x^5y)^2

Step 3. Use Multiplication Distributive Property

-3 * 16x^4 * 4^2(x^5)^2y^2

Step 4. Simplify 4^2 to 16

-3 * 16x^4 * 16(x^5)^2y^2

Step 5. Use the Power Rule

-3 * 16x^4 * 16x^10y^2

Step 6. Take out the constants

-(3 * 16 * 16)x^4x^10y^2

Step 7. Simplify 3 *16 * 16 to 768

-768x^4x^10y^2

Step 8. Use the Product Rule

-768x^4 + 10y^2

Step 9. Simplify 4 + 10 to 14

-768x^14y^2

Answer 2

​-3(2x)⁴(4x⁵y)² = When a power is raised to a power the exponents have to be multiplied.

​-3(2⁴x⁴)(4²x⁽⁵*²⁾y²) = We can take out the constants.

=-3*16*16(x⁴)(x¹⁰y²) = We can group the same variables​.

=-768(x⁴x¹⁰)(y²) = When multiplying two powers that have the same base, you have to add the exponents.​

​=-768x⁽⁴⁺¹⁰⁾y² = -768x¹⁴y²

​Answer : -768x¹⁴y²

Hope this helps!​​​​​

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