Rational exponents, step by step

A fractional exponent is a root and a power in one symbol: the bottom says which root, the top says what to raise it to.

The question

What is 8 to the power 4/3?

8^(4/3)

∛8 = 2
2⁴ = 16
8^(4/3) = 16
  1. The BOTTOM of the exponent says which root to take, so the cube root of 8 comes first. Root before power, always — the other order works and makes the numbers enormous.
  2. The TOP says what to raise it to. 2 to the power 4 is 16.
  3. So 8^(4/3) is 16.

How it works.

  1. 01

    The BOTTOM of the exponent says which root to take, so the cube root of 8 comes first. Root before power, always — the other order works and makes the numbers enormous.

  2. 02

    The TOP says what to raise it to. 2 to the power 4 is 16.

  3. 03

    So 8^(4/3) is 16.