Three Rules, and Their Evil Twins

You'll learnto build the exponent rules by counting factors, and to kill the popular fake versions with one number.

An exponent is a count of factors, and every rule in this topic is a statement about what happens to that count when rows of factors are pushed together, copied out, or flipped underneath. Watch the blocks do the arithmetic, then watch one identity most students refuse to believe: shifting an exponential sideways is exactly the same as stretching it upward. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · b^m·bⁿ = b^m+n · 5^x+2 = 25·5^x · v3

an exponent counts factors · the rules count them for you

Before you start

What you're looking at

Powers drawn as rows of small blocks, one block per factor, that push together, copy out and flip below a line marked one.

The question

When do exponents add, and when do they multiply?

Step 1 / 12