Rational exponentsMixed
Name: Date:
Work out each one. Take the root first, then raise it.
1161/4 =
2165/4 =
384/3 =
443/2 =
52161/3 =
61251/3 =
72561/4 =
8641/3 =
9161/2 =
1095/2 =
Rational exponents worksheets
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. These free printable worksheets keep every answer a whole number, so the notation is the only new thing on the page.
Kid stuck on one? You don’t just get the sheet.
Rational exponents
The answer key prints on a separate page.
What's on this sheet
Root first, and the walk says why rather than just which. Both orders give the same answer — ∛(8²) is ∛64 = 4 as well — but only one of them can be done in your head. Taking the root first keeps every number small; raising first turns 1000^(2/3) into the cube root of a million.
Why this sheet works
Nothing here is computed with a fractional power. `Math.pow(1000, 1/3)` is 9.999999999999998 in a browser, so a sheet that worked its own answers out would print a key that is wrong by inspection. Every question is built forwards from a whole base, a whole root and a whole power.
How this one works
One question from this sheet, worked through a step at a time.
16^(1/4)
⁴√16 = 2
16^(1/4) = ⁴√16
16^(1/4) = 2
- The BOTTOM of the exponent says which root to take, so the 4th root of 16 comes first. Root before power, always — the other order works and makes the numbers enormous.
- The top is 1, so there is nothing left to raise — a exponent of 1/4 IS the 4th root, written the other way.
- So 16^(1/4) is 2.