Rational Exponents Test – Algebra 1 Math (Printable PDF)

Question 1 Multiply monomials (2 points)

Simplify (6a⁴b)(−2a³b⁵).

Question 2 Divide monomials (2 points)

Simplify 20m⁹n³5m⁴n⁸ and write the answer with positive exponents.

Question 3 Power of a product (2 points)

Simplify (−2x³y)⁴.

Question 4 Evaluate rational exponents (2 points)

Evaluate (a) 27^2/3 (1 point) and (b) 4^−3/2 (1 point).

Question 5 Radical and exponent forms (2 points)

(a) Write ∛(x⁷) with a rational exponent. (1 point) (b) Write a^5/2 as a radical. (1 point)

Question 6 Simplify square roots (3 points)

Simplify each radical (variables are nonnegative). (a) √98 (1 point) (b) √45 (1 point) (c) √(20x⁶) (1 point)

Question 7 Rectangle with radicals (3 points)

A rectangle has width √12 cm and length √27 cm.

(a) Write each side in simplest radical form. (1 point) (b) Find the exact area. (1 point) (c) Find the exact perimeter. (1 point)

Question 8 Radioactive decay (3 points)

The mass of a sample in grams is A = 80(1/2)^t/4 after t hours. (a) Find the mass at t = 12. (1 point) (b) Find the exact mass at t = 2 and approximate it. (1 point) (c) Explain what the 4 in the exponent means. (1 point)

Question 9 Locate a root (1 point)

Between which two consecutive integers does √55 lie? Use the number line.