Writing multiplication expressions using exponents

An exponent is a counting job before it is a multiplication job. The base tells you which number repeats; the exponent tells you how many times it appears as a factor. That is all.

The sheet tests exactly that. Items a to d give your child the product and ask for the power, so the work is pure counting. Items e to g flip it: five ready-made powers, and only one with the right base and the right count. The wrong ones are not random. They swap base and exponent (7³⁴ for 34⁷) or reverse the digits (79⁶ for 97⁶), the two slips sixth graders really make.

This is the first expressions standard of Grade 6, 6.EE.A.1: write and evaluate numerical expressions with whole-number exponents.

Start with item a and stay quiet for a moment. If your child writes 5³, hold back the correction. Ask, "How many 5s can you touch?" Then let them tap each one with a pencil. The count lands on four, and the mistake explains itself: three x signs sit between four factors.

Item c is the long one, with seven 7s, so suggest a tally mark under each factor. For e to g, try a different question: "Which choices have the wrong base?" Crossing those out first leaves two or three powers to compare, and the exponent decides.

When they reach 97⁶, slow down. Read the base aloud together, digit by digit.

Exponents show up wherever something repeats. At dinner, ask, "If we double this recipe three times, how many batches?" That is 2 x 2 x 2, or 2³, so eight. A square kitchen tile that measures 4 inches on each side covers 4 x 4, or 4², square inches.

For a story, read One Grain of Rice by Demi together. A girl asks a raja for one grain of rice, doubled every day for 30 days, and the pile grows past a billion grains. Your child can write each day's amount as a power of 2.

Close by naming the work, not the score: "You counted every factor before you wrote a power." Next in this series, the missing exponent or base sheet asks the same question in reverse.