Algebra 1 Exponent Rules and Radicals Quiz: 10 Questions with Explanations

A \(x^{10}\)B \(x^{24}\)C \(x^{2}\)D \(2x^{10}\)

Add the exponents when you multiply powers with the same base: 4 + 6 = 10.

A \(x^{10}\)B \(x^{7}\)C \(x^{25}\)D \(5x^{2}\)

For a power of a power, multiply the exponents: 2 · 5 = 10.

A \(-3\)B \(\frac{1}{3}\)C \(0\)D \(-\frac{1}{3}\)

Each step divides by 3, so after 1 comes 1/3. A negative exponent means a reciprocal.

A \(1\)B \(1\frac{1}{4}\)C \(\frac{1}{4}\)D \(5\)

5⁰ = 1 and 2⁻² = 1/4, so the sum is 1 and 1/4.

A \(25\sqrt{2}\)B \(2\sqrt{5}\)C \(5\sqrt{2}\)D \(10\sqrt{5}\)

50 = 25 · 2, and the square root of 25 is 5.

A 9B 18C 3D 6

The cube root of 27 is 3, and 3 squared is 9. Computing 27 · 2/3 gives 18, a common error.

A Rational, exactly 2.2B Rational, exactly 2.5C Irrational, about 5D Irrational, about 2.24

5 is not a perfect square, so its square root is irrational, between 2 and 3.

A \(\sqrt{16} + 1\)B \(0.25 + \frac{1}{3}\)C \(\sqrt{49} \cdot \frac{1}{7}\)D \(\frac{1}{2} + \sqrt{3}\)

A rational number plus an irrational number is irrational. The other expressions are rational.

A \(\sqrt[3]{x^{4}}\)B \(\sqrt[4]{x^{3}}\)C \((\sqrt{x})^{3}\)D \(\sqrt[4]{x}\)

The denominator 4 is the root index and the numerator 3 is the power.

A \(P = 40 + 40t\)B \(P = 2 \cdot 40^{t}\)C \(P = 40 \cdot 2^{t}\)D \(P = 40 \cdot t^{2}\)

The starting value is 40 and the growth factor is 2, so P = 40 · 2^t.