Logs and Exponents

Rational to Radical

100

Write x^1/2 as a radical

What is the √x?

200

Write (5x)^2/3 as a radical

What is the ³√(5x)²?

300

Write 4^-5/6 as a radical

What is 1/⁶√(4)⁵?

400

Write 1/64^-5/6 as a radical

What is ⁶√(64)⁵?

500

Write 6(9x)^1/3 as a radical

What is 6 times the cube root of (9x)?

Log to Exponent

100

Evaluate: log₅25

What is 2?

200

Evaluate: log₅1/25

What is -2?

300

Evaluate: log₁₆4

What is 1/2?

400

Evaluate: log_1/21/8

What is 3?

500

Evaluate: log₃₆1/6

What is -1/2?

Exponent to Log

100

Write 3² = 9 as a log

What is log₃9 = 2?

200

Write the square root of 25 = 5 as a log

What is log₂₅5 = 1/2?

300

Write 4^-2 = 1/16 as a log

What is log₄1/16 = -2

400

Write (1/2)³ = 1/8 as a Log

What is log_1/21/8 = 3?

500

Write 64^-1/3 = 1/4 as a log

Log₆₄1/4 = -1/3

Exponent Rules

100

Simplify: x² * 3x³

What is 3x⁵?

200

Simplify (5x)³

What is 125x³?

300

Simplify: 2(x³)^-2

What is 2/x⁶?

400

Simplify: (3w³/5w⁵⁾

What is 3/5w²?

500

Simplify (2^-2x³y^-4/x⁰)²

What is x⁶/16y⁸?

Radical to Rational

100

Write √x as a rational exponent.

What is x^1/2?

200

Write ³√x as a rational exponent.

What is x^1/3?

300

Write ³√x⁵ as a rational exponent.

What is x^5/3?

400

Write 2 ³√3 as a rational exponent.

What is 24^1/3?

500

Write 2√3 as a rational exponent.

What is 12^1/2?