Math Practice Problems - Roots Of Exponential Expressions

Roots Of Exponential Expressions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=5, Mode=exponent

Find the exponent.

Correct Answer

Your Answer

₅ 2²⁰

Solution

₅ 2²⁰

= (2²⁰) ^{^(¹/₅)} = 2^{(20 * ¹/₅)} = 2^{( ²⁰/₅)} = 2⁴

Correct Answer

Your Answer

₃ 3⁹

Solution

₃ 3⁹

= (3⁹) ^{^(¹/₃)} = 3^{(9 * ¹/₃)} = 3^{( ⁹/₃)} = 3³

Complexity=8, Mode=value

Find the value of the given expression.

Correct Answer

Your Answer

₅ 4²⁰

Solution

₅ 4²⁰

= (4²⁰) ^{^(¹/₅)} = 4^{(20 * ¹/₅)} = 4^{( ²⁰/₅)} = 4⁴ = 256

Correct Answer

Your Answer

₅ 2¹⁰

Solution

₅ 2¹⁰

= (2¹⁰) ^{^(¹/₅)} = 2^{(10 * ¹/₅)} = 2^{( ¹⁰/₅)} = 2² = 4

Complexity=8, Mode=variable

Simplify the given expression. Use '^' to indicate 'to the power of' and omit any 1's as coefficients in front of variable expressions.

Correct Answer

Your Answer

7⁶x⁶

Solution

7⁶x⁶

= (7⁶x⁶)^{^(¹/₂)} = 7^{(6 * ¹/₂)} x^{(6 * ¹/₂)} = 7^(⁶/₂) x^(⁶/₂) = 7³x³ = 343x³

Correct Answer

Your Answer

₃ 5⁶x⁹

Solution

₃ 5⁶x⁹

= (5⁶x⁹)^{^(¹/₃)} = 5^{(6 * ¹/₃)} x^{(9 * ¹/₃)} = 5^(⁶/₃) x^(⁹/₃) = 5²x³ = 25x³

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