5th Grade Exponents and Powers worksheets

About this worksheet

5. NBT. A. 2 asks fifth graders to use whole-number exponents to denote powers of ten and to explain the pattern in the number of zeros, and this worksheet builds directly on that, then extends the same notation to small squares and cubes the way the task calls for. An exponent tells you how many times a number is used as a factor, so 10^3 means 10 x 10 x 10, which is 1,000, and the 3 is not a number you add or subtract, it is a count of how many tens are multiplied together. Saying it as "multiply 10 by itself three times" is the shortcut almost everyone uses, and it is the reason 10^1 confuses children: it is one ten, multiplied by nothing at all. Children often confuse the exponent with the number of zeros to "add," which works for powers of ten by coincidence but breaks immediately for 5^2 or 3^3, so this worksheet asks about both powers of ten and small squares and cubes side by side, so the shortcut is not mistaken for the rule.

Questions cover the vocabulary too: which part of 6^2 is the base and which is the exponent, since a fifth grader who cannot name the parts cannot talk about the pattern. A few questions connect the notation to something concrete, like the number of tiles in a square patio, or ask your child to compare two powers that turn out equal, which is a genuine surprise the first time you see it. Encourage your child to say the multiplication out loud, "5 times 5," rather than just recalling that squaring means multiplying a number by itself.

What your child will learn

• Compute powers of ten using exponent notation
• Explain what the exponent in a power of ten tells you
• Compute small squares and cubes, such as 5^2 and 3^3
• Name the base and the exponent in an expression
• Describe how multiplying by a power of ten shifts a decimal point