Free Online Exponents Calculator

This exponents calculator works out x raised to the power of n for any base and exponent — positive, negative, or decimal. For small whole numbers it shows the full expanded multiplication, not just the final answer.

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Exponent Calculator

xn = ?

Exponent Rules Reference

RuleFormula
Product rulexm · xn = xm+n
Quotient rulexm ÷ xn = xm−n
Power of a power(xm)n = xm·n
Negative exponentx−m = 1 ÷ xm
Zero exponentx0 = 1
Exponent of onex1 = x

Answer

Solution:

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Opening this link fills in x and n and shows this result automatically.

Enter a base and exponent and the answer, worked out step by step, will appear here.

What Does an Exponent Actually Mean?

An exponent is just shorthand for repeated multiplication. Writing 34 saves you from writing 3 × 3 × 3 × 3 every time — the exponent tells you how many times the base multiplies itself.

Worked Example: 3 to the Power of 4

34 = 3 × 3 × 3 × 3 = 81

What a Negative Exponent Means

A negative exponent doesn't make the result negative — it flips the base into a fraction instead. x−n is just 1 divided by xn.

3−4 = 1 ÷ 34 = 1 ÷ 81 ≈ 0.012346

A Common Mix-Up: −4² vs. (−4)²

These two look almost identical but give different answers, and it trips up a lot of people. Without parentheses, the minus sign is applied after the exponent, so it means "the negative of 4 squared." With parentheses, the negative sign is part of the base itself.

−4² = −(4 × 4) = −16
(−4)² = (−4) × (−4) = 16

This calculator treats a negative value you type into the base field as if it had parentheses around it — entering −4 for x always calculates (−4)n.

A Few Special Cases

  • Anything to the power of 1 is just itself: x1 = x.
  • Anything (except 0) to the power of 0 equals 1: x0 = 1.
  • 0 to the power of 0 is defined as 1 by convention, not calculated the usual way.

Using the Share, Print and Copy Options

  • Share: After you calculate, a ready-made link appears with your exact x and n baked in. Send it to anyone and their page opens already filled in with your result showing.
  • Print: Prints just your inputs and the worked solution — no ads, menus or surrounding page clutter.
  • Copy: Copies a plain-text version of the answer straight to your clipboard, ready to paste anywhere.

Frequently Asked Questions (FAQs)

A negative exponent is a rule about position, not sign — it means "take the reciprocal," not "make it negative." x to the power of negative n is defined as 1 divided by x to the power of n, which is why 3 to the power of negative 4 comes out as a small positive decimal, not a negative number.

Yes. A decimal exponent is really a root in disguise, since fractional exponents represent roots (for example, raising a number to the power of 0.5 is the same as taking its square root). This calculator handles decimal exponents directly.

The full expansion is only shown for small whole-number bases and exponents, since a base like 347 raised to the 12th power would need an unreadably long multiplication chain. Larger or decimal values still get a correct answer, just without the step-by-step expansion.

That combination is undefined, since it would require dividing by zero. The calculator will flag this as an invalid input rather than return a number.

No. The link only encodes the exact base and exponent you entered, so anyone opening it sees the same calculation you did, nothing more.

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