Integer Exponents Practice Problems

Knowing the exponent rules and applying them quickly under time pressure are two different skills. The Integer Exponents lesson covers where every rule comes from; this practice set is where that knowledge turns into speed, with unlimited fresh problems and instant right/wrong feedback.

How the difficulty levels work

Difficulty	What it drills	Example
Easy	Evaluate directly
Medium	Product/Quotient Rule, or
Hard	Power-of-power, chains, sign traps	vs

Easy is single-power evaluation with small bases and exponents 2 through 4, plus an occasional to keep the Zero Exponent Rule reflexive from the start.

Medium rotates between the Product Rule (), the Quotient Rule () — which sometimes lands on a negative net exponent — and standalone negative exponents like , where the answer is always a fraction.

Hard mixes four problem shapes: power-of-a-power (), power of a product (), three-term product/quotient chains, and the versus sign distinction — the single most common exponent mistake, drilled directly instead of hoping it never comes up.

Worked examples

One example at each difficulty level, solved the way the practice set expects.

Easy. Evaluate .

Medium. Evaluate and .

Same base, so subtract the exponents: . A negative exponent is a reciprocal: .

Hard. Compare with , then evaluate .

Without brackets, the exponent applies only to the : . With brackets, the whole is squared: . For a power of a power, multiply the exponents: .

Using the practice problems

Adjust the difficulty and question count, and a new set appears without any wait. Enter each answer as a whole number or a fraction — both 1/16 and 0.0625 are accepted for the same answer.

Check Answers totals the score and points to any problem that needs another attempt
Show Answers reveals the entire key instantly, good for double-checking paper work
Print Worksheet outputs a neat printable version, good for offline practice or handouts

The rules these practice problems drill

Rule	Statement
Product Rule
Quotient Rule
Power Rule
Power of a Product
Zero Exponent
Negative Exponent

See the Integer Exponents lesson for where each of these comes from and a full worked derivation.

Common mistakes to watch for

Adding exponents instead of multiplying, or vice versa. (add), but (multiply) — mixing these up is the single most common error in this practice set’s Medium and Hard problems.

Treating a negative exponent as a negative result. , a positive fraction. The minus sign means “reciprocal,” never “negative value.”

Dropping the parentheses on a negative base. , but — genuinely different numbers. Check which one a problem is actually showing before you answer.

Combining exponents on different bases. The Product and Quotient Rules only combine same-base terms — there’s no shortcut for something like .

Where to go next

Once these rules feel automatic, the Rational Exponent Practice Problems extends the same rules to fractional exponents and roots. For the full derivations and worked examples behind every rule drilled here, see the Integer Exponents lesson.

Frequently Asked Questions

What rules does this practice set actually drill?+

All eight from the Integer Exponents lesson: the Product, Quotient, and Power Rules; Power of a Product; the Zero and Negative Exponent Rules; and, at Hard difficulty, the sign difference between (−b)^n and −b^n.

Why do some answers come out as fractions?+

Any expression whose net exponent ends up negative — like 4^3 ÷ 4^5 — evaluates to a fraction by the Negative Exponent Rule, so the correct answer really is something like 1/16, not a decimal or an error.

How do I type a fraction answer?+

Type it exactly as it looks, like 1/16, or as its decimal equivalent, like 0.0625. Both are accepted.

Why does Hard difficulty include problems like −5^2?+

Confusing −5^2 with (−5)^2 is one of the most common exponent mistakes there is, so a portion of Hard problems drill it directly: without parentheses, the exponent binds to 5 only, giving −25; with parentheses, it binds to −5, giving 25.

Are the exponents ever fractions in this practice set?+

No, every exponent here is a whole number, positive, zero, or negative. Fractional exponents are practiced separately in the rational exponent practice set.

What if I've never seen these rules before?+

Start with the Integer Exponents lesson, which derives every rule this practice set uses from scratch with worked examples, then come back here to build speed and accuracy.

Does the practice set ever stop producing new problems?+

None. You're free to generate as many sets as you'd like, at no cost and with no login.

xⁿInteger Exponents Practice Problems