Fractional indices
Work out the value of the power.
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A fraction in the index is another way of writing a root: the denominator tells you which root, the numerator which power. 8^(2/3) means “the cube root of 8, then squared”: ∛8 = 2 and 2² = 4. The same laws of indices work for these powers as for whole-number indices.
What does this generator do?
On the easy level you work out values like 8^(2/3) or 32^(2/5). On the medium level negative indices and fractions as the base appear (write the answer as a fraction), as well as writing a root as a power, for example ∛(a²) = a^(2/3). On the hard level you simplify expressions like a^(1/2) · a^(1/3), (a^(2/3))^(3/4) or √a · ∛a.
How to use it
1) Rewrite a^(m/n) as the root ⁿ√(aᵐ) — take the root first, then the power, so the numbers stay small. 2) A negative index means “one over” (the reciprocal). 3) When multiplying powers, add the indices; when dividing, subtract them; for a power of a power, multiply them. Write a fraction with a slash, for example 5/6.