Negative Exponents Practice Problems

Why a negative exponent means reciprocal, and never a negative value, is explained in full in the Negative Exponents lesson. This practice set turns that single rule into speed, with unlimited fresh problems across numbers, products, quotients, and variable expressions.

How the difficulty levels work

Difficulty	What it drills	Example
Easy	Evaluate directly, including a negative base
Medium	Negative exponent on a quotient or product
Hard	Chained negative exponents, or a coefficient-variable expression at a chosen

Easy evaluates directly with small whole-number bases, occasionally with a negative base to keep the even/odd sign rule reflexive from the start.

Medium applies the negative exponent rule to a quotient (flip the fraction, drop the minus sign) or a product, so the reciprocal is taken of more than a single number.

Hard mixes two problem shapes: chaining two negative exponents on the same base with the Product Rule, and evaluating a coefficient-variable expression like at a specific , which tests that the coefficient never moves.

Worked examples

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

Easy. Evaluate and .

A negative exponent means a reciprocal: , and . The sign comes from the odd power, not from the negative exponent.

Medium. Evaluate .

Flip the fraction, then square: .

Hard. Evaluate , then at .

Add the exponents: . In only has the negative exponent, so it’s .

Using the practice problems

Pick a difficulty level and how many you want, and the set generates instantly. Enter each answer as a fraction or its decimal equivalent — both 1/9 and 0.111 are accepted for the same answer.

Check Answers grades the set on the spot and calls out anything incorrect
Show Answers uncovers every solution in one click, handy for reviewing handwritten answers
Print Worksheet creates a clean, printable page suited for classroom handouts or homework

The rules these practice problems drill

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

See the Negative Exponents lesson for the full reasoning behind this rule and why it never produces a negative result on its own.

Common mistakes to watch for

Treating the negative exponent as a negative number. , a small positive fraction, never .

Moving a coefficient that has no exponent attached. In , the stays exactly where it is — only becomes a fraction.

Forgetting a negative base’s sign still applies. ; the negative base carries through exactly as it would with a positive exponent.

Distributing a negative exponent over a sum. The negative exponent rule only ever applies to a single factor, a product, or a quotient — never to two terms being added or subtracted.

Where to go next

Once the reciprocal rule feels automatic on its own, the Exponent Rules Practice Problems combines it with the product, quotient, and power rules in a single problem. For the full derivation and every sign-related mistake this rule invites, see the Negative Exponents lesson.

Frequently Asked Questions

Why do almost all the answers come out as fractions?+

A negative exponent means reciprocal, and the reciprocal of a whole number greater than 1 is a proper fraction. is the correct, fully simplified answer — not a decimal approximation and not an error.

How do I type a fraction answer, including a negative one?+

Type it exactly as it looks, like 1/9, or as its decimal equivalent, like 0.111. For a negative fraction, put the minus sign on the numerator, like -1/8.

Why does (-3)^-2 come out positive but (-3)^-3 come out negative?+

The negative exponent only controls the reciprocal, not the sign — the sign of the final answer is decided entirely by whether the exponent is even or odd, exactly the same as it would be for a positive exponent. An even exponent always gives a positive result; an odd exponent keeps the base's negative sign.

Do the coefficient-and-variable problems ever move the coefficient?+

No. A negative exponent only relocates the factor it is directly attached to, so in a problem like evaluating 5x^-2, the 5 always stays exactly where it is — only the x^-2 part becomes a fraction.

How is this different from the Integer Exponent Practice Problems?+

The Integer Exponent practice set rotates through all eight integer exponent rules, with negative exponents as just one of several rotating subtypes. This practice set drills the negative exponent rule specifically and exclusively, at every difficulty level, including its interaction with products, quotients, and variables.

Do I need an account to generate unlimited sets?+

No cap. Every set is created fresh on demand, free of charge and login-free.

x⁻ⁿNegative Exponents Practice Problems