1.2 Exponents

The use of calculators or other technologies are strictly prohibited for this assignment.

1 Exponents as Repeated Multiplication

  1. Fill in the blanks to show that you can use repeated addition to solve a multiplication problem: \(2 \times 3 = 2 + \_\_ + \_\_ = 3 + \_\_ = \_\_\).

  2. Fill in the blanks to show that you can use repeated multiplication to solve an exponent problem: \(2^3 = 2 \times \_\_ \times \_\_ = \_\_\).

  3. Calculate \(1^8\).

  4. Calculate \((-3)^3\).

  5. Calculate \(6^2\).

2 The Zeroeth Power and Negative Exponents

  1. Calculate \(2^0\).

  2. Calculate \(1^0\).

  3. Calculate \((-1)^0\).

  4. Calculate \(6^{-1}\).

  5. Calculate \((-6)^{-2}\).

  6. Simplify \(x^{-5}\) for \(x \neq 0\).

3 Multiplying and Dividing Powers

  1. Simplify \(\frac{a^2}{a^4}\).

  2. Simplify \(x^{-3}x^5\).

  3. Simplify \(\frac{12^{-5}}{12^{-7}}\).

4 Powers of Products and Quotients

  1. Simplify \((a^{-8} b^{3})^{-2}\).

  2. Simplify \((a^{-2} 8^{7})^{2}\).

5 Fractional Exponents

  1. Calculate \(16^{1/2}\).

  2. Calculate \(8^{1/3}\).

  3. Calculate \(9^{3/2}\).

  4. Simplify \(\frac{a^{1/2}}{a}\).