Math
Grades 7–9 · Algebra 1

The rules of exponents.

The exponent rules look like a list to memorize, but every one of them comes from what an exponent actually means: repeated multiplication. Study Butler builds the rules from that idea, so your kid can rebuild any rule they forget.

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Here is what that looks like.

Study Butler will not print the answer. It points at the next step and lets your kid take it.

An example. The butler answers the question with a question.

what is x squared times x cubed.

write out what each one means. how many x's in x squared, how many in x cubed.

two and three.

so how many x's are being multiplied in total. that number is your new exponent.

Where students get stuck.

The same few mistakes come up again and again. Here is where the butler slows things down.

01Multiplying the exponents when you should add

For x squared times x cubed, students often multiply 2 and 3. Study Butler has them write the x's out, which makes it obvious you add the counts.

02Mishandling a power raised to a power

A quantity like (x squared) cubed is where adding and multiplying get confused. The butler walks through what the outer exponent is actually doing to the inner one.

03Forgetting that anything to the zero power is one

Raising to the zero power feels strange. Study Butler shows the pattern of dividing powers down, so zero lands naturally instead of as a rule to accept.

Bring the problem they're stuck on.

Type it, say it, or snap a photo. Study Butler walks your kid to the answer one question at a time, so they learn it instead of copying it.

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Questions parents ask.

Why do you add exponents when multiplying?
Because the exponent counts how many times the base is multiplied, and multiplying two powers just stacks the counts together. Study Butler has your kid write the bases out so the addition is obvious.
What is anything raised to the power of zero?
It is always one, for any nonzero base. The cleanest way to see it is the pattern of dividing by the base as the exponent drops. The butler walks your kid down that pattern.