Algebra 2 Radicals and Rational Exponents Quiz: 10 Questions with Explanations

A \(250\)B \(\frac{125}{3}\)C \(5\)D \(25\)

Take the cube root first: 5. Then square it: 25. Multiplying 125 by 2/3 or stopping after the root are common errors.

A \(y^{5/4}\)B \(y^{4/5}\)C \(y^{9}\)D \(y^{1/20}\)

The index 5 goes in the denominator and the power 4 in the numerator.

A \(40.5\)B \(9\)C \(\frac{1}{81}\)D \(3\)

The exponent 1/2 means square root, and sqrt(81) = 9. Dividing 81 by 2 or using a fourth root are mistakes.

A \(\frac{1}{4}\)B \(-4\)C \(-8\)D \(4\)

A negative exponent gives a reciprocal: 1 / 16^(1/2) = 1/4. The negative sign does not make the answer negative.

A \(x^{3/16}\)B \(x^{1/3}\)C \(x\)D \(x^{4}\)

Add exponents: 1/4 + 3/4 = 1. Multiplying exponents instead gives 3/16.

A \(4^{1/2} = 8\)B \(2^{1/2} = 4\)C \(4^{1/2} = \frac{1}{2}\)D \(4^{1/2} = 2\)

The point (4, 2) means that when x = 4, y = 2, so 4^(1/2) = 2.

A \(8x^{2}\)B \(4x^{2}\)C \(4x^{3}\)D \(\frac{16x^{9}}{3}\)

Apply 2/3 to each factor: 8^(2/3) = 4 and (x^3)^(2/3) = x^2.

A \(x = 4\)B \(x = 12\)C \(x = 2\)D \(x = \sqrt{8}\)

Raise both sides to 2/3: x = 8^(2/3) = 4. Check: 4^(3/2) = 8.

A \(4\)B \(8\)C \(2\)D \(64\)

16^(1/4) is the fourth root of 16, which is 2 because 2^4 = 16.

A \(It equals -2\)B It equals 2C It is not a real numberD It equals -4

The cube root of a negative number is real: (-2)^3 = -8. Odd roots exist for negative numbers; even roots do not.