Three Rules, and Their Evil Twins

You'll learnto build the three exponent rules from repeated factors and spot their fake versions.

Every exponent rule has a popular wrong version, and the wrong versions feel just as natural as the right ones. Watch the real rules work as blocks that stack, tile, and flip — then watch one identity most students refuse to believe: a horizontal shift of an exponential IS a vertical stretch.

8 STEPS · 6 QUICK CHECKS · b^m·bⁿ = b^m+n · 5^x+2 = 25·5^x · v2

b^m · b^n = b^(m+n)

Before you start

What you're looking at

Exponent expressions shown as blocks of repeated factors that stack, tile, and flip.

The question

When do exponents add, and when do they multiply?

Watch for

Add exponents when bases multiply; multiply them when a power is raised to a power; there is no rule for adding bases.

Step 1 / 8