Exponents with decimal bases

Here a decimal is the base, so the place of the decimal point matters as much as the digits.

• Write the decimal as a fraction over 10, 100 or 1,000
• Raise the top and the bottom to the power: (35 ÷ 10)³ = 42,875 ÷ 1,000
• Count decimal places: (0.0033)² has eight, so it is 0.00001089
• Remember that any power 1 keeps the number and any power 0 gives 1

Evaluating numerical expressions with exponents is 6.EE.A.1.

Follow the worked example in the top left corner first.

• Rewrite each decimal as a fraction before multiplying.
• Multiply the whole numbers, then divide by the power of ten.
• In the two-choice part, estimate first: 0.4 x 0.4 x 0.4 must be smaller than 0.4.

Page two shows each fraction step, so your child can find the exact line where an answer went wrong.

• Multiplying base by exponent: (0.4)³ is 0.064, not 1.2.
• Losing decimal places: (0.4)³ has three places, so 0.064, not 0.64.
• Treating a power 0 as zero: (13.00025)⁰ = 1.

Note: on page one, the right choice for (9.5)⁴ is misprinted as "8,1450.625"; the true value is 8,145.0625, as the second page shows. Next, try exponents with fractional bases.