A power is repeated multiplication
Writing aⁿ means multiplying a by itself n times: 2¹⁰ = 1024. A negative exponent gives the reciprocal (2⁻² = 1/4), and an exponent of zero always gives one.
Power and root calculators
Exponents, square roots and roots of any degree. Three calculators that show how taking a root is simply raising to a fractional power.
A root is a fractional power
The nth root of a is a^(1/n). That is why the fifth root of 1024 is 1024^(0.2) = 4. This one identity replaces all the separate rules for roots.
Frequently asked questions
Raise the number to the power 1/n. For the fifth root of 1024, work out 1024^(1/5) = 4.
For an odd degree yes — the cube root of −8 is −2. For an even degree there is no real solution.
It follows from the rule for dividing powers with the same base, and holds for every base other than zero.
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