Properties of Exponents

Properties of Exponents

1. Product of powers rule

When multiplying two bases having the same value, keep the bases the same and then add the exponents together to get the solution.

2² × 2⁴ =?

So the base values are both two, keep them the same, and then add the exponents (2 + 4) together.

3²× 3⁴ = 3⁶

2. Quotient of powers rule

Multiplication and division are opposites to each other much the same, the quotient rule is opposite of the product rule and when dividing two bases having the same value, keep the base same, and then subtract the exponent values.

4⁵ ÷ 4³ =?

Both bases in this equation are four, keep them the same. Then, take the exponents and subtract the divisor from the dividend.

4⁵ ÷ 4³ = 4²

Finally, simplify the equation if needed:

4² = 4 × 4 = 16

3. Power of a power rule

This equation is where power is being raised by another power.

(𝒙²)² =?

Multiply the exponents together and keep the base the same.

(𝒙²)² = 𝒙⁴

4. Power of a product rule

When any base is multiplied by an exponent, distribute or seperate the exponent to each part of the base.

(𝒙𝑦)² =?

In this equation, the power of two needs to be distributed to both the 𝒙 and the 𝑦 variables.

(𝒙𝑦)² = 𝒙²𝑦²

This rule applies if there are exponents attached to the base as well.

(𝒙²𝑦²)² = 𝒙⁴𝑦⁴

5. Power of a quotient rule

A quotient that is you are dividing two quantities. In this rule, raising a quotient by a power. similar to the power of a product rule, the exponent needs to be seperate from all values within the brackets it’s attached to.

(𝒙/𝑦)² =?

(𝒙𝑦)² = \(𝒙^2\over y^2\)

Also, read the Quadratic Equations