Chapter 10

In Exercises \(65-70,\) simplify. Then use a calculator to evaluate the expression. $$ \left(-1 \cdot 3^{2}\right)^{3} $$

Solve the equation. $$ (a-3)(a+5)^{2}=0 $$

Multiply the fractions. $$\frac{1}{4} \cdot \frac{1}{4}$$

Solve the equation. \(|x-5|=7\)

Simplify the expression. Write your answer as a power. $$ (0.5 w)^{2} $$

Find the product. \((2 x-4)(4 x-2)\)

Simplify. $$ \frac{2}{3} \cdot \frac{6}{9} \div \frac{11}{3} $$

Determine whether the ordered pair is a solution of the system of linear equations. $$ \begin{aligned} &x+9 y=-11\\\ &-4 x+y=-30 \quad(7,-2) \end{aligned} $$

In Exercises \(65-70,\) simplify. Then use a calculator to evaluate the expression. $$ \left(2^{2} \cdot 2^{2}\right)^{2} $$

Solve the equation. $$ (b+4)(b-3)(2 b-1)=0 $$

Multiply the fractions. $$\frac{2}{3} \cdot \frac{2}{3}$$

Solve the equation. \(|x+6|=13\)

Simplify the expression. Write your answer as a power. $$ 9^{3} \cdot 9^{5} $$

Find the product. \((x+10)(x+10)\)

Simplify. $$ \frac{1}{2} \div \frac{1}{9} \cdot \frac{2}{3} $$

Determine whether the ordered pair is a solution of the system of linear equations. $$ \begin{aligned} &2 x+6 y=22\\\ &-x-4 y=-13 \quad(-5,-2) \end{aligned} $$

In Exercises \(65-70,\) simplify. Then use a calculator to evaluate the expression. $$ \left(3^{2} \cdot 2^{3}\right)^{3} $$

Add. $$ 3.7+1.04+5.2 $$

Multiply the fractions. $$\frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3}$$

Solve the equation. \(|4 x+3|=9\)

Simplify the expression. Write your answer as a power. $$ \left(4^{2}\right)^{4} $$

Find the product. \((3 x+5)(2 x-3)\)

Simplify. $$ \frac{1}{2} \cdot \frac{4}{9} \cdot \frac{5}{6} $$

Determine whether the ordered pair is a solution of the system of linear equations. $$ \begin{aligned} &-2 x+7 y=-41\\\ &3 x+5 y=15 \quad(-10,3) \end{aligned} $$

The population \(P\) of Alabama (in thousands) for 1995 projected through 2025 can be modeled by \(P=4227(1.0104)^{t},\) where \(t\) is the number of years since \(1995 .\) Find the ratio of the population in 2025 to the population in \(2000\)

Add. $$ 6.7+0.356+4 $$

Multiply the fractions $$ \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} $$

Graph the inequality. \(x+y<9\)

Simplify the expression. Write your answer as a power. $$ b^{2} \cdot b^{5} $$

Simplify. $$ \frac{8}{9} \div \frac{9}{8} \cdot \frac{8}{9} $$

Determine whether the ordered pair is a solution of the system of linear equations. $$ \begin{aligned} &-5 x-8 y=28\\\ &9 x-2 y=48 \quad(4,-6) \end{aligned} $$

Add. Write the answer as a mixed number in simplest form. $$ \frac{12}{11}+1 \frac{3}{11} $$

Add. $$ 7.421+5+8.09 $$

Multiply the fractions. $$\frac{2}{5} \cdot \frac{2}{5} \cdot \frac{2}{5}$$

Graph the inequality. \(y-3 x \geq 2\)

Simplify the expression. Write your answer as a power. $$ \left(4 c^{2}\right)^{4} $$

Simplify. $$ \frac{2}{3} \cdot \frac{4}{5} \cdot \frac{6}{7} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &x-y=2\\\ &2 x+y=1 \end{aligned} $$

Add. Write the answer as a mixed number in simplest form. $$ \frac{2}{5}+3 \frac{3}{5} $$

Add. $$ 8.1+0.2+3.56 $$

Multiply the fractions. $$\frac{3}{4} \cdot \frac{3}{4} \cdot \frac{3}{4}$$

Graph the inequality. \(y-4 x \leq 10\)

Simplify the expression. Write your answer as a power. $$ (2 t)^{4} \cdot 3^{3} $$

Simplify. $$ \frac{12}{15} \cdot \frac{3}{4} \div \frac{1}{7} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &x-2 y=10\\\ &3 x-y=0 \end{aligned} $$

Add. Write the answer as a mixed number in simplest form. $$ 1 \frac{2}{3}+\frac{1}{6} $$

Add. $$ 6.012+2.9+5.6314 $$

Multiply the fractions. $$ \frac{5}{8} \cdot \frac{5}{8} \cdot \frac{5}{8} $$

Find the reciprocal. 18

Simplify the expression. Write your answer as a power. $$ \left(-w^{4}\right)^{3} $$