Find the missing exponent or base practice

This page runs powers backward: the result is known, and one part of the power is missing.

• Find a base by trying small numbers: 5⁴ = 625, so the base is 5
• Find an exponent by multiplying step by step: 2, 4, 8, 16, 32 means 2⁵ = 32
• Count the zeros of powers of ten: 10,000,000 = 10⁷
• Use the special cases: any nonzero number to the power 0 is 1, and to the power 1 is itself

Evaluating whole-number exponents is 6.EE.A.1; powers of ten also revisit 5.NBT.A.2.

A list of the first squares and cubes (4, 9, 16, 25 … and 8, 27, 64, 125) on scrap paper saves time.

• Start with the solved example: 3 x 3 x 3 = 27.
• For each missing base, guess, multiply, then adjust up or down.
• For each missing exponent, keep a tally of how many times you multiplied.

Check the 26 red answer boxes on page two against your child's work.

• Dividing by the exponent: for ?² = 729, 729 ÷ 2 is not the base; 27 x 27 = 729 is.
• Counting digits instead of zeros: 10,000,000 has eight digits but seven zeros, so it is 10⁷.
• Thinking a power of 0 gives 0: 150,005⁰ = 1, while 1,352¹ = 1,352.

Next, move to powers of decimals and fractions in this series.