Algebra 1 Exponent Rules and Radicals Test with Point Values (PDF)

1. Evaluate \(2^{5} \cdot 2^{-2}\). (1 point)
2. Evaluate \(\frac{(3^{2})^{3}}{3^{4}}\). (1 point)

Simplify \((4x^{3}y^{2})^{2}\).

Simplify \(\frac{x^{-3}y^{4}}{x^{2}y}\) and write the answer with positive exponents.

The square has area 98 square inches. Write its side length in simplest radical form.

Evaluate each expression.

1. \(64^{1/3}\) (1 point)
2. \(9^{3/2}\) (1 point)

1. Write \(x^{3/4}\) as a radical. (1 point)
2. Write \(\sqrt[5]{y^{2}}\) with a rational exponent. (1 point)

The number line shows \(\sqrt{11}\) and 3.

1. Classify \(\sqrt{81}\) as rational or irrational. (1 point)
2. Classify \(\sqrt{11}\) as rational or irrational. (1 point)
3. Explain why \(3 + \sqrt{5}\) is irrational. (1 point)

A population is modeled by \(P = 50 \cdot 3^{t}\) where \(t\) is in hours.

1. Find \(P(0)\). (1 point)
2. Find \(P(4)\). (1 point)
3. Find \(t\) when \(P = 1350\). (1 point)

A student wrote \((2x)^{3} = 2x^{3}\). Explain the error and give the correct result.