Grade 8 · Math

8th grade Negative exponents and the laws of exponents worksheet

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Negative exponents and the laws of exponents

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

In math club, Ari meets (1/2)^-3. What is the value of (1/2)^-3?
In math club, Bo meets (2/3)^-2. What is the value of (2/3)^-2?
In math club, Jun meets (-2)^-3. What is the value of (-2)^-3?
Kira's padlock tag shows 7^-3 × 7^-5 = 7^?. What is the missing exponent?
Noah's puzzle card shows 6^-2 × 6^7 = 6^?. What is the missing exponent?
Pia's worksheet shows (5^-2)^3 = 5^?. What is the missing exponent?
Tala's worksheet shows (6^-1)^-5 = 6^?. What is the missing exponent?
Ari's worksheet asks for 9^-2 ÷ 9^3 as one power. How do you write 9^-2 ÷ 9^3 as a single power of 9?
Ari's padlock tag shows 9^-6 × 9^2 = 9^?. What is the missing exponent?
Bo's robot screen shows 3^-2 ÷ 3^5 = 3^?. What is the missing exponent?

Negative exponents and the laws of exponents. Every version has 10 questions, and the answer key prints on the second page.

I can find the value of a power with a negative exponent: 2⁻³ = 1 ÷ (2 × 2 × 2) = 1/8, including fraction and negative bases.
I can multiply, divide and raise powers of the same base when exponents are negative, keeping every sign.
I can work a mixed expression such as (2⁻³)² ÷ 2⁴ step by step, and I know a⁰ = 1.

Standard: 8.EE.A.1

negative exponent: The factors sit below a fraction bar: 2⁻³ = 1 ÷ (2 × 2 × 2).

strip of factors: A power written out: 2³ is 2 × 2 × 2.

cancel: A factor on top and the same one below divide to 1.

zero exponent: Every factor cancels, so 1 is left: 6⁰ = 1.

single power: One base and one exponent, such as 4⁻⁴.

Your child made the answer negative because the exponent was negative. A negative exponent means 1 over the power: 2^-3 = 1 ÷ 8.

Your child multiplied the base by the exponent. An exponent counts factors: 2^-3 = 1 ÷ (2 × 2 × 2).

Your child worked out the power but forgot that the minus sign puts it under 1.

Ask: what does the minus in the exponent tell you to do?

What is the most common mistake with negative exponents and the laws of exponents?

Your child made the answer negative because the exponent was negative. A negative exponent means 1 over the power: 2^-3 = 1 ÷ 8.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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