Grade 8 · Math

8th grade Exponent laws with letters, like (3x³y⁻²)³ worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

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Exponent laws with letters, like (3x³y⁻²)³

Grade 8 Math Worksheet

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

Exponent laws with letters, like (3x³y⁻²)³. Every version has 10 questions, and the answer key prints on the second page.

I can multiply, divide and raise powers of the same letter, with negative exponents: d⁶ × d⁻² = d⁴.
I can simplify a monomial: (3x³y⁻²)³ = 27x⁹y⁻⁶ and 28x⁵y² ÷ (7x⁻¹y⁸) = 4x⁶y⁻⁶, keeping negative exponents in the answer.
I can rewrite a monomial with only positive exponents, moving only the part with the negative exponent.

Standard: state-only (CCSS 8.EE.A.1 is numerical expressions only)

monomial: A number times letters with exponents, such as 3x³y⁻².

coefficient: The number in front: 3 in 3x³y⁻².

like bases: Powers of the same letter, such as x³ and x⁻².

raise every part: (3x²)⁴ gives the 3, and the x, the power 4.

Your child multiplied the exponents when two powers of the same letter were multiplied. Write the strips out together and count: x^3 × x^4 = x^7.

Your child added the exponents in a power of a power. (x^2)^3 is 3 copies of x^2, so the exponents multiply: x^6.

Your child added the exponents when dividing. Dividing cancels factors, so the exponents subtract, sign and all: x^2 ÷ x^-5 = x^7.

What is the most common mistake with exponent laws with letters, like (3x³y⁻²)³?

Your child multiplied the exponents when two powers of the same letter were multiplied. Write the strips out together and count: x^3 × x^4 = x^7.

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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