8th Grade Properties of Integer Exponents Quiz: 10 Questions with Explanations

A \(7^{5}\)B \(7^{3}\)C \(7^{-4}\)D \(7^{-3}\)

Add the exponents: 4 + (-1) = 3. Subtracting in the wrong order gives 7^-3, and 7^5 comes from changing the sign of the second exponent.

A \(\frac{1}{25}\)B \(-25\)C \(-10\)D \(\frac{1}{10}\)

\(5^{-2} = \frac{1}{5^{2}}\). A negative exponent is a reciprocal, not a negative number.

A \(6^{3}\)B \(6^{6}\)C \(6^{12}\)D \(1^{6}\)

Subtract the exponents: 9 – 3 = 6. Dividing the bases gives the wrong 1.

A \(0 \text{ and } -1\)B \(1 \text{ and } -\frac{1}{2}\)C \(1 \text{ and } \frac{1}{2}\)D \(0 \text{ and } \frac{1}{2}\)

Each step to the right divides by 2: 2, then 1, then one half.

A \(4^{5}\)B \(4^{8}\)C \(12^{6}\)D \(4^{6}\)

Power of a power: multiply the exponents, 2 x 3 = 6. Adding gives the wrong 5.

A \(\frac{1}{9}\)B \(-9\)C \(-\frac{2}{3}\)D \(9\)

Flip the base and use a positive exponent: \(3^{2} = 9\).

A \(7^{6}\)B \(14^{5}\)C \(7^{5}\)D \(7^{1}\)

Five sevens multiplied together is \(7^{5}\). Multiplying 2 x 3 gives the wrong 6.

A \(n = -3\)B \(n = 3\)C \(n = 5\)D \(n = -5\)

Add exponents: n + 4 = 1, so n = -3.

A \(2^{6}\)B \(2^{5}\)C \(2^{9}\)D \(2^{8}\)

Area = \(\left(2^{3}\right)^{2} = 2^{6} = 64\) square feet.

A \(9^{0}\)B \(0^{1}\)C \(\left(-4\right)^{0}\)D \(1^{-5}\)

\(0^{1} = 0\). The others all equal 1: any nonzero base to the zero power, and 1 to any power.