Integer Exponents

Powers: Shorthand for Repeated Multiplication

Which of the following is not equal to the other three?

Multiplying and Dividing Same-Base Powers

Evaluate $3^{2}\cdot 3^{3}$.

Evaluate $\dfrac{10^{6}}{10^{3}}$.

Examples: Combine Same Bases First, Then Compute

True or false: $2^{3}\cdot 5^{3}=10^{6}$.

Zero and Negative Exponents

Which of the following is undefined?

Evaluate $2^{-4}\cdot 2^{6}\cdot 2^{-1}$.

Power of a Power: Multiply the Exponents

Examples: Powers of Powers and Stacking

Evaluate $(3^{2})^{-2}\cdot 3^{5}$.

Look-Alike Contrast: Sum or Product in the Numerator

Evaluate $\dfrac{2^{5}\cdot 2^{-3}}{2^{4}\cdot 2^{-6}}$.

Evaluate $3^{4}\cdot 2^{3}\cdot 3^{-2}$.

Evaluate $3^{3}\cdot 2^{-2}\cdot 3^{-1}\cdot 2^{4}$.

What are the five laws of integer exponents (for $b\neq0$)?

Why is $b^{0}=1$ stipulated (for $b\neq0$)? Start from the fraction $\dfrac{b^{m}}{b^{m}}$.