Exponents with fractional bases

Raising a fraction to a power means raising both of its parts.

• Power the numerator and the denominator separately: (3/8)² = 9/64
• Write the repeated factors to stay organized: 5 x 5 x 5 over 6 x 6 x 6
• Simplify at the end: (10/4)¹ = 10/4 = 5/2
• Use the shortcut that any nonzero fraction to the power 0 equals 1

This is 6.EE.A.1, with fraction multiplication from 5.NF.B.4 doing the heavy lifting.

Work through the solved grid square with your child before starting.

• Copy each power as a numerator power over a denominator power.
• Write out the factors on the second line, then multiply.
• Reduce the fraction if the top and bottom share a factor.

The second page boxes each final fraction; use it to check both the value and the simplifying.

• Powering only the top: (1/2)⁷ is 1/128, not 1/2.
• Multiplying by the exponent: (3/4)⁴ is 81/256, not 12/16.
• Copying the fraction for a power 0: (6/8)⁰ = 1, not 6/8.

Note: for (10/4)², the choices 25/4 and 100/16 are equal; the key ticks 25/4 because the heading asks for the most correct, that is simplest, answer. Next, explore negative exponents.