How do I type a negative exponent?

Put it in parentheses, x^(-2), or paste a superscript such as x⁻². Typing x^-2 without parentheses asks you to add them, so a minus sign is never read as subtraction by accident. Exponents are literal integers from -20 to 20.

Which exponent rules does it apply?

All of the integer-exponent rules, with exact coefficients: x^3 * x^4 = x^7 (product rule), x^5/x^2 = x^3 (quotient rule), (x^2)^3 = x^6 (power of a power), (2x)^3 = 8x^3 (power of a product), (x/y)^(-2) = y^2/x^2 (negative power of a quotient) and x^0 = 1 (zero exponent). The result is the same as applying these rules by hand, written as one fraction.

How do I simplify using only positive exponents?

Choose Simplify expression. The result is always one fraction whose numerator and denominator have only positive powers, so x^(-3) is written as 1/x^3 and 6x^(-2)/(3y^(-3)) as 2y^3/x^2. Coefficients are reduced as exact fractions.

Why does the answer list x ≠ 0?

A zero or negative power needs a nonzero base, and so does a variable that was divided by. x^(-3) means 1/x^3, which is undefined at x = 0, so the condition stays with the answer even when the variable disappears from it: x^0 simplifies to 1 only where x ≠ 0.

Can I simplify fractions with exponents?

Yes. Type the numerator and denominator in parentheses, such as (x^5y^2)/(x^2y^3). Common powers cancel exactly, giving x^3/y, and the domain keeps the original denominator's restriction.

Which exponents are not supported?

Fractional or rational exponents such as x^(1/2), variable exponents such as 2^x, and powers outside -20 to 20. Radicals and logarithms are also outside this tool.

Simplify Exponents

Simplify products, quotients and powers of variables with integer exponents from -20 to 20, and read the answer with positive exponents only. The page opens on (2x^3y^(-2))^2/(4x^(-1)), which becomes x^7/y^4, with x ≠ 0 and y ≠ 0 kept because both sat under a negative power.

ExpressionExact rational algebra

Your expression

24 / 2,000 charactersCtrl or ⌘ + Enter to run

Up to 3 real variables, integer powers -20 to 20 and one optional equals sign. Expand distributes products; Simplify also cancels shared polynomial factors.

Supported syntax and limits

Use +, -, *, /, parentheses and powers such as x^2 or x². Integers, fractions and finite decimals are exact.

2xy means 2*x*y. For a longer name, use brackets: 2[rate] + [cost]. Names have up to 24 characters and start with a letter.

Multiplication and division run left to right: 1/2x means (1/2)*x. Use 1/(2x) for a denominator of 2x.

Put a negative power in parentheses, x^(-2), or type x⁻²; the result is written with positive exponents. Zero and negative powers require a nonzero base: x^0 = 1 only where x ≠ 0.

One equals sign, as in 2(x + 1) = x/x, simplifies each side separately. The equation is not solved. Functions, radicals, scientific notation and variable or fractional exponents are unsupported.

Expansion is bounded to 2,000 terms and 1,000 digits in each exact coefficient numerator or denominator. An arithmetic budget, 80 nesting levels and a 10-second worker limit prevent unbounded work. Cancel or press Escape to keep your input.

Check a substitution (optional)

Value of xValue of y

Exact values agree

Original expression: 128/81
Result expression: 128/81

The exact rational values agree at this permitted substitution. A single substitution is a check, not a proof of equivalence.

Simplified expressionExample preview

Original domain

y ≠ 0
x ≠ 0

These conditions remain after cancellation.

Inspect original divisors and zero- or negative-power bases

y (base of a negative power) ≠ 0x (base of a negative power) ≠ 0

Read the expression
Use exact rational coefficients and real variables x, y. Adjacent letters multiply; multiplication and division are evaluated left to right.
Preserve the original domain
Keep y ≠ 0; x ≠ 0 before cancelling any factors. A zero or negative power also requires a nonzero base.
Distribute and collect
Expand finite integer powers and distributive products. Add coefficients only when every variable has the same power.
(x^7)/(y^4)
Reduce the rational form
The expanded numerator and denominator have no further nonconstant common polynomial factor. Rational coefficients are reduced exactly.
(x^7)/(y^4)

Result terms2

Variables2

Domain conditions2

ArithmeticExact rational

Complete text and LaTeX output

Complete expression and domain

(x^7)/(y^4)
Domain: y ≠ 0; x ≠ 0

Both formats retain the original domain conditions. Select this text to copy manually.

Example preview. Edit the expression or run it to make your own result.

Try a worked example

Accuracy. Exact rational-expression algebra within 2,000 input characters, three real variables, integer powers from -20 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions and radicals are unsupported, and an equation's two sides are simplified separately, not solved. A result is a canonical rational form, not a claim of the shortest possible expression.

Common questions

How do I type a negative exponent?: Put it in parentheses, x^(-2), or paste a superscript such as x⁻². Typing x^-2 without parentheses asks you to add them, so a minus sign is never read as subtraction by accident. Exponents are literal integers from -20 to 20.
Which exponent rules does it apply?: All of the integer-exponent rules, with exact coefficients: x^3 * x^4 = x^7 (product rule), x^5/x^2 = x^3 (quotient rule), (x^2)^3 = x^6 (power of a power), (2x)^3 = 8x^3 (power of a product), (x/y)^(-2) = y^2/x^2 (negative power of a quotient) and x^0 = 1 (zero exponent). The result is the same as applying these rules by hand, written as one fraction.
How do I simplify using only positive exponents?: Choose Simplify expression. The result is always one fraction whose numerator and denominator have only positive powers, so x^(-3) is written as 1/x^3 and 6x^(-2)/(3y^(-3)) as 2y^3/x^2. Coefficients are reduced as exact fractions.
Why does the answer list x ≠ 0?: A zero or negative power needs a nonzero base, and so does a variable that was divided by. x^(-3) means 1/x^3, which is undefined at x = 0, so the condition stays with the answer even when the variable disappears from it: x^0 simplifies to 1 only where x ≠ 0.
Can I simplify fractions with exponents?: Yes. Type the numerator and denominator in parentheses, such as (x^5y^2)/(x^2y^3). Common powers cancel exactly, giving x^3/y, and the domain keeps the original denominator's restriction.
Which exponents are not supported?: Fractional or rational exponents such as x^(1/2), variable exponents such as 2^x, and powers outside -20 to 20. Radicals and logarithms are also outside this tool.

Exact rational-expression algebra within 2,000 input characters, three real variables, integer powers from -20 to 20, 2,000 expanded terms and 1,000 digits per coefficient numerator or denominator. Original undefined points are retained, including 0^0; functions and radicals are unsupported, and an equation's two sides are simplified separately, not solved. A result is a canonical rational form, not a claim of the shortest possible expression.