Rational Exponents Test – Algebra 2 Math (Printable PDF)

Question 1 Evaluate (2 points)

Evaluate each expression.

1. ∛(−216)
2. 32^3/5
3. 81^−3/4
4. ⁴√(625)

(0.5 point each)

Question 2 Changing forms (2 points)

Complete each part.

1. Write ⁵√(x³) with a rational exponent. (1 point)
2. Write y^7/4 as a radical. (1 point)

Question 3 Simplify radicals (3 points)

Simplify. Assume all variables are positive.

1. √(98x⁶) (1 point)
2. ∛(81y⁵) (2 points)

Question 4 Exponent rules (2 points)

Simplify. Assume x > 0 and a > 0.

1. x^3/2 · x^1/4x^−1/4 (1 point)
2. (16a^4/3)^3/4 (1 point)

Question 5 Radical expressions (3 points)

Simplify.

1. 3√20 + √45 (1 point)
2. Rationalize the denominator: 103 − √2 (2 points)

Question 6 Radical equation and its graph (3 points)

The graphs of y = √(5x + 1) and y = x − 1 are shown.

1. Solve √(5x + 1) = x − 1 algebraically and check each candidate. (2 points)
2. Use the graph to explain which candidate is extraneous. (1 point)

Question 7 Two radicals (3 points)

Solve √(x + 3) + √x = 3. Check the answer.

Question 8 Falling time (2 points)

The time t (seconds) for a stone to fall h feet is t = √h / 4. The graph is shown.

1. How high is a cliff if the fall takes 3.5 seconds? (1 point)
2. How long does a 144-foot fall take? (1 point)