Skill: exponent-rules

Exponent Rules Tutor Help

Stuck on exponent rules? Review the core ideas, read answers to common questions, and send a question to a tutor.

1 Quick recap

Exponents count factors: x^3 means three x’s multiplied. Multiply powers by adding exponents, divide by subtracting, raise a power to a power by multiplying. x^0 = 1, and x^(-a) = 1/x^a.

Core ideas

Multiply powers: ADD exponents.
Divide powers: SUBTRACT exponents.
Power of a power: MULTIPLY exponents.
The power distributes to coefficients: (2x^3)^2 = 8x^6.
x^0 = 1; x^(-a) = 1/x^a.

2 Questions students ask

The questions a tutor hears most about this skill.

Do I add or multiply the exponents for x^3 times x^4?

Add: 3 + 4 = 7, so x^7. You multiply exponents only for a power of a power, like (x^3)^4 = x^12. A quick expansion check settles it: 3 factors plus 4 factors is 7 factors.

What does a negative exponent actually do?

It moves the power across the fraction bar: 2^(-3) = 1/2^3 = 1/8. It never makes the answer negative — the minus is a direction, not a sign.

Why is anything to the power 0 equal to 1?

From the quotient rule: x^3/x^3 = x^(3-3) = x^0, but any nonzero number divided by itself is 1. So x^0 must be 1.

3 Ask a tutor

Stuck on a problem? Send it in — a tutor will walk you through it.

Demo form: this contact form is a demonstration only — it does not send anywhere and has no backend connected. Nothing you type leaves this page.