# 1.2 Exponents

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

## 1 Exponents as Repeated Multiplication

<iframe width="300" height="auto" src="https://www.youtube.com/embed/XZRQhkii0h0" title="Introduction to exponents | Pre-Algebra | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

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

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

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c) Calculate $1^8$.

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d) Calculate $(-3)^3$.

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e) Calculate $6^2$.

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## 2 The Zeroeth Power and Negative Exponents

<iframe width="300" height="auto" src="https://www.youtube.com/embed/Tqpcku0hrPU" title="Negative exponent intuition | Pre-Algebra | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) Calculate $2^0$.

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b) Calculate $1^0$.

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c) Calculate $(-1)^0$.

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d) Calculate $6^{-1}$.

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e) Calculate $(-6)^{-2}$.

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f) Simplify $x^{-5}$ for $x \neq 0$.

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## 3 Multiplying and Dividing Powers

<iframe width="300" height="auto" src="https://www.youtube.com/embed/CZ5ne_mX5_I" title="Multiplying &amp; dividing powers (integer exponents) | Mathematics I | High School Math | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) Simplify $\frac{a^2}{a^4}$.

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b) Simplify $x^{-3}x^5$.

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c) Simplify $\frac{12^{-5}}{12^{-7}}$.

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## 4 Powers of Products and Quotients

<iframe width="300" height="auto" src="https://www.youtube.com/embed/dC1ojsMi1yU" title="Powers of products &amp; quotients (integer exponents) | Mathematics I | High School Math | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

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

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

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## 5 Fractional Exponents

<iframe width="300" height="auto" src="https://www.youtube.com/embed/lZfXc4nHooo" title="Basic fractional exponents | Exponent expressions and equations | Algebra I | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) Calculate $16^{1/2}$.

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b) Calculate $8^{1/3}$.

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c) Calculate $9^{3/2}$.

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d) Simplify $\frac{a^{1/2}}{a}$.

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