Product Rule for Exponents

Laws of exponents - Power of a Product Rule

by J. Gomez

Power of Product Shortcut?!!

Instead of repeating it three times you can just distribute the exponent to everything inside the group.

(x²y)⁵ = x^2*5 y^1*5 = x¹⁰y⁵

Further Example

• Now lets combine power of a product with power of a power

• We know that if we have a power outside the parenthesis we distribute it to everything inside the parenthesis.

• We also know that if we distribute a power to another power we multiply these powers.

Multiple Choice

Simplify the following expression:

(3y⁴)²

• 9y⁸

• 9y⁶

• 6y⁸

• 6y⁶

Multiple Choice

$$\left(2xy\right)^5$$  

• $$2x^5y^5$$  

• $$2^5x^5y^5$$  

• $$2xy^5$$  

• $$2\left(x^5y^5\right)$$  

Multiple Choice

$$\left(3^2ab^0\right)^4$$  

• $$3^6a^5b^4$$  

• $$3^8ab^0$$  

• $$3^8a^4$$  

• $$3^8a^4b^0$$  

Multiple Choice

Simplify the following expression:

(2x³y)⁶

• 2x¹⁸y⁶

• 64x¹⁸y⁶

• 64x³y⁶

• 2x³y⁶

Multiple Choice

Simplify the following expression:

(3x⁴y⁵)²

• 9x⁸y¹⁰

• 6x⁸y¹⁰

• 3x⁸y¹⁰

• x⁸y¹⁰