MathGPT ScientificFree scientific workspace
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Evaluate powers and exponents, with steps
Use the free exponent calculator to work through the number relationship, preserve exact values, and check the result with estimation. Calculate with natural scientific notation, reusable history, angle modes, memory, probability functions, and familiar calculator layouts.
Arithmetic
Exponent Calculator explained
The short version
- An exponent counts how many copies of the base get multiplied, so 2⁵ is 2 × 2 × 2 × 2 × 2 = 32.
- When the bases match you add the powers to multiply and subtract them to divide.
- A negative power means one over that power, and any base to the power 0 is 1.
The formula this page uses
aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿ a⁰ = 1 a⁻ⁿ = 1 / aⁿ
What each part means
SymbolWhat it means
a — The baseThe number being multiplied by itself. It never changes when you use these rules.
m and n — The exponentsWhole numbers, negative numbers or fractions. They are the only part that gets added or subtracted.
aᵐ — A powerRead as 'a to the m'. For m = 2 say 'squared', for m = 3 say 'cubed'.
a⁻ⁿ — A negative power1 divided by aⁿ. It makes the number small, not negative.
Show your work: a full example
- Simplify 2⁵ × 2³ ÷ 2⁴2⁵ × 2³ ÷ 2⁴
- Same base, so add the powers for the multiply2⁵⁺³ = 2⁸
- Same base, so subtract for the divide2⁸⁻⁴ = 2⁴
- Work out the value2⁴ = 16
- Check the long way32 × 8 = 256
- Finish the check256 ÷ 16 = 16
A second, different case
- A different case: zero, negative and minus signs3⁻²
- A negative power flips the number over3⁻² = 1 ÷ 3² = 1 ÷ 9 = 0.111…
- Why anything to the power 0 is 15³ ÷ 5³ = 125 ÷ 125 = 1, and the rule says 5³⁻³ = 5⁰
- An even power on a negative base(−2)⁴ = (−2)(−2)(−2)(−2) = 16
- An odd power on a negative base(−2)³ = −8
- The same digits without brackets−2⁴ = −(2 × 2 × 2 × 2) = −16
Copy-ready example
2⁵ × 2³ ÷ 2⁴
Simplify 2⁵ × 2³ ÷ 2⁴
Questions about the Exponent Calculator
Why does anything to the power 0 equal 1?
Follow the pattern down: 2⁴ = 16, 2³ = 8, 2² = 4, 2¹ = 2. Each step halves the answer, so the next one has to be 2 ÷ 2 = 1. The same pattern works for every base, which is why 7⁰ and 1000⁰ are both 1.
What about 0⁰?
It has no agreed value. The pattern for 0ⁿ pushes toward 0, while the pattern for n⁰ pushes toward 1, and they disagree. Most calculators answer 1 because that is convenient for algebra, but a maths class will usually call it undefined.
What does a fractional exponent mean?
It means a root. Since 9^(1/2) × 9^(1/2) = 9¹ = 9, the value 9^(1/2) must be the square root, which is 3. In the same way 8^(1/3) = 2, and 8^(2/3) = 4, because you cube-root first and then square.
Why is (−2)⁴ different from −2⁴?
The brackets decide what the base is. In (−2)⁴ the base is −2, and four minus signs multiply to a plus, giving 16. In −2⁴ the base is only the 2, so you work out 2⁴ = 16 and then apply the minus, giving −16.
How to use a scientific calculator accurately
The calculator executes the expression entered; mathematical judgment still determines the correct expression, mode, and interpretation.
Set the angle mode
Use degrees for degree-labelled angles and radians for calculus or unit-circle work unless the problem states otherwise. A correct key sequence in the wrong mode produces a wrong value.
Group the expression
Use parentheses around numerators, denominators, exponents, and negative substitutions. Read the full display before evaluating.
Keep precision until the end
Reuse the stored answer instead of a rounded display value during multi-step work, then round once to the requested precision and units.
Estimate and verify
Predict sign and scale, use identities or inverse operations, and compare a second entry when the result matters.
About the calculator layouts
The MathGPT, TI-84 Plus-style, HP Prime-style, Casio fx-CG50-style, and Casio fx-9860GIII-style key arrangements share one independent calculation engine. They provide familiar practice layouts and do not emulate proprietary firmware or imply affiliation with those manufacturers.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.