#### Chapter 1 Elementary Arithmetic

Section 1.4 Powers and Roots

# 1.4.3 Exercises

##### Exercise 1.4.18
Calculate the following powers:
1. ${\left(-\frac{3}{5}\right)}^{4}$$=$ .

2. ${\left({2}^{-2}\right)}^{-3}$$=$ .

3. ${\left(-\frac{1}{2}\right)}^{0}$$=$ .

##### Exercise 1.4.19
Simplify the following expressions using the exponent rules and by reducing the results. You don't need to evaluate the powers:
1. $\frac{\left(-2{\right)}^{7}}{\left(-2{\right)}^{5}}$$=$ .

2. ${6}^{2}·{3}^{-2}$$=$ .

3. $\frac{{64}^{3}}{{8}^{3}}$$=$ .

4. ${\left(\frac{3}{4}\right)}^{\frac{1}{3}}·{\left(\frac{3}{4}\right)}^{\frac{2}{3}}$$=$ .

##### Exercise 1.4.20
Calculate the following roots (here, the result is always an integer):
1. $\sqrt[3]{3}·\sqrt[3]{9}$$=$ .

2. $\sqrt[3]{343}$$=$ .

##### Exercise 1.4.21
Simplify the following expressions and write each as a reduced fraction containing no powers:
1. $\frac{{3}^{3}·{6}^{3}}{9·{2}^{3}·{4}^{3}}$$=$ .

2. ${3}^{2}·{9}^{-3}·{27}^{6}·{27}^{-2}$$=$ .