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Grade 11 · Math · Algebra 2

11th grade Exponential equations: rewrite with the same base worksheet

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Exponential equations: rewrite with the same base

Grade 11 Math Worksheet

NameDate

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

  1. Kira solves 9^x = 27 on a math club card. What is x?

  2. Milo solves 125^x = 25 in a math book. What is x?

  3. Pia solves 4^(x + 3) = 32 by writing both sides as powers of 2. What is x?

  4. Ren solves 8^(x − 2) = 16 by writing both sides as powers of 2. What is x?

  5. Tala solves 25^(x + 1) = 125 by writing both sides as powers of 5. What is x?

  6. Zee solves 4^x = √8 on a math club card. What is x?

  7. Ari solves 9^x = ∛3 on the class board. What is x?

  8. Bo solves 25^x = 1/√5 in a math book. What is x?

  9. Jun rewrites 25^x = 125 so both sides are powers of 5. Which equation is right?

    • 5^(2x) = 5⁴
    • 5^(x + 2) = 5³
    • 2^(5x) = 3⁵
    • 5^(2x) = 5³

  10. Kira rewrites 8^(x + 1) = 4 so both sides are powers of 2. Which equation is right?

    • 2^(3x + 3) = 2³
    • 2^(3x + 1) = 2²
    • 2^(3x + 3) = 2²
    • 2^(x + 4) = 2²
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11th grade Exponential equations: rewrite with the same base worksheet – printable
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About this worksheet

Exponential equations: rewrite both sides with the same base. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can solve 2^(x + 1) = 32 by finding the row of 32 in the × 2 table.
  • I can write both sides as powers of one base, like 9 = 3² and 27 = 3³, and then set the exponents equal.
  • I can handle fractions, roots and brackets in the exponent, and an x on both sides.

Standard: A-REI.A.1, F-LE.A.4 (related)

Words to know

exponential equation: An equation with x in an exponent, like 2^(x + 1) = 32.

same base: Both sides written as powers of one number, like 3^(2x) = 3³.

equate the exponents: Set the two exponents equal once the bases match.

power of a power: (3²)^x: the exponents multiply, giving 3^(2x).

negative exponent: A power below row 0: 2⁻⁴ = 1/16.

fraction exponent: A root as a power: √8 = 8^(1/2) = 2^(3/2).

Common mistakes

Divided the two numbers (27 ÷ 9) instead of writing both as powers of one base.

Found the right row but gave it as x, forgetting the number added to x in the exponent.

Moved a number across the equals sign without changing its sign. Solve x + 2 = 5 and x − 2 = 5 together and compare.

What to say

Ask: 9 is 3 to what power, and 27 is 3 to what power?

Ask: if x + 1 = 5, what is x?

Questions parents ask

What is the most common mistake with exponential equations: rewrite with the same base?

Divided the two numbers (27 ÷ 9) instead of writing both as powers of one base.

How can I help my child with exponential equations: rewrite with the same base?

Ask: 9 is 3 to what power, and 27 is 3 to what power?

Are these 11th 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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