x³ · x⁴
- 1.Same base, multiplied → add the exponents (Product rule)
x⁷
Spot-check at x = 2: 8 · 16 = 128 and 2⁷ = 128 ✓.
Exponents — rules applied, results spot-checked
Simplify powers or solve exponential equations. Every step names the rule it uses, and every answer is checked numerically at real values — so a rule mix-up can never slip through quietly.
- ✓100% free — no paywall, ever
- ✓No sign-up, no app
- ✓Every answer verified before you see it
In short
An exponent calculator simplifies powers and solves exponential equations using the exponent rules: multiply same bases by adding exponents, divide by subtracting them, and raise a power to a power by multiplying. VerifySolve names the rule behind every step and spot-checks each result numerically, so a simplification is never just asserted — it is tested.
The exponent rules
Five rules cover nearly every exponent problem in school algebra. The calculator names the rule at each step — learn the names and the homework starts reading itself.
Product rule
Quotient rule
Power of a power
Negative & zero exponents
Worked examples — simplified, solved, checked
Simplifications are verified at x = 2 and x = 3; equations are verified by substitution. Same checks the live solver runs on your input.
(2x²)³
- 1.Raise every factor to the 3rd power (Power of a product)
- 2.2³ · (x²)³ = 8 · x⁶ (Power of a power)
8x⁶
Spot-check at x = 2: (2·4)³ = 512 and 8·64 = 512 ✓.
2^x = 32
- 1.Rewrite 32 as a power of 2: 32 = 2⁵
- 2.Same base on both sides → the exponents are equal
x = 5
Verified: 2⁵ = 32 ✓ — exactly the right side.
x² = 16
- 1.Undo the square by taking the square root of both sides
x = 4 or x = −4
Verified both ways: 4² = 16 ✓ and (−4)² = 16 ✓. Even powers have two roots.
Common mistakes — and how to dodge them
Adding exponents across different bases
2³ · 3² is not 6⁵. The product rule needs the SAME base. With different bases, evaluate each power separately: 8 · 9 = 72. The calculator refuses to merge unlike bases — copy that discipline.
(x²)³ = x⁵
Adding here is the classic mix-up. A power of a power multiplies: (x²)³ = x⁶. When unsure, expand it: (x²)(x²)(x²) — the six x’s settle the argument.
Reading 2⁻² as −4
A negative exponent is an instruction (take the reciprocal), not a sign for the answer: 2⁻² = 1/4. If your simplified answer flips negative just because an exponent did, check again.
Two kinds of exponent problems
Simplify — no equals sign
The answer is a tidier expression: one base, one exponent, coefficient in front. The rules do the work, and the numeric spot-check (same value at x = 2 and x = 3) proves the tidy version is worth exactly as much as the messy one.
Solve — with an equals sign
The answer is a value of x. The exact method: get the same base on both sides, then set the exponents equal. If the right side is not an exact power of the base, the honest answer needs a logarithm — and the solver will say exactly that instead of faking it.
Exponent Calculator — questions
What exponent problems can this calculator do?
Two kinds. Simplifying: products, quotients and powers of monomials (x³ · x⁴, (2x²)³) plus exact numeric powers like 2¹⁰. Solving: exponential equations that reduce to the same base on both sides (2^x = 32, 3^(x+1) = 27) and power equations like x³ = 27 — all solved exactly.
How are exponent answers verified?
Numerically, at concrete values: the original and simplified expressions are evaluated at x = 2 and x = 3 and must agree exactly. For evaluated powers, the answer is multiplied back out factor by factor. A match at several points is real evidence, not a guess.
What about 2^x = 30, where the answer is not a whole number?
That needs logarithms (x = log₂ 30), which this engine does not do yet — and it tells you so, with the estimate, instead of dressing up a decimal as an exact answer. Same-base problems cover most of Algebra 1 and much of Algebra 2.
Why does (x²)³ equal x⁶ and not x⁵?
Because (x²)³ means x² · x² · x² — three groups, each contributing 2 to the exponent total: 2 + 2 + 2 = 6. Powers of powers multiply exponents; plain products add them. Mixing those two rules up is the most common exponent error.
Does a negative exponent make the answer negative?
No — a negative exponent means “take the reciprocal”: 2⁻² = 1/2² = 1/4, a positive fraction. The calculator shows the reciprocal step explicitly so the meaning sticks.
Is the exponent calculator free?
Yes — free, no sign-up, no app, full steps and verification included.
Keep solving
Algebra Calculator →
Equations, systems, simplifying and factoring — verified.
Factoring Calculator →
Factor trinomials with the expand-back proof.
Derivative Calculator →
Where exponent rules meet calculus: the power rule, verified numerically.
Equation Solver →
Any equation type, routed to the right method automatically.
A note on honest use: VerifySolve is built for learning. Use the steps to understand the method, then close the tab and try one on your own — that is where the grade actually comes from. If your teacher or school has a policy on calculators, follow it.