Chapter 8

Write your answer as a power or as a product of powers. $$ (-3 a)^{5} \cdot(4 a)^{2} $$

Rewrite the expression with positive exponents. $$(-9)^{0} x$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{m^{3} \cdot m^{5}}{m^{2}} $$

Evaluate the expression. $$24+m^{3} \text { when } m=5$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(7 \times 10^{-3}\right) \cdot\left(8 \times 10^{-4}\right) $$

Write your answer as a power or as a product of powers. $$ -(3 x)^{2} \cdot\left(7 x^{4}\right)^{2} $$

Rewrite the expression with positive exponents. $$(-4 x)^{-3}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{\left(r^{3}\right)^{4}}{\left(r^{3}\right)^{8}} $$

Evaluate the expression. $$\frac{a^{2}-b^{2}}{a b} \text { when } a=3 \text { and } b=5$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(6 \times 10^{5}\right) \cdot\left(2.5 \times 10^{-1}\right) $$

Write your answer as a power or as a product of powers. $$ 2 x^{3} \cdot(3 x)^{2} $$

Rewrite the expression with positive exponents. $$(-10 a)^{0}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{-6 x^{2} y}{2 x y^{3}}\right)^{3} $$

Evaluate the expression. $$4 a^{2}+11 \text { when } a=5$$

Evaluate the expression. $$x^{6}-1 \text { when } x=1.2$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(1.2 \times 10^{-6}\right) \cdot\left(2.3 \times 10^{4}\right) $$

Write your answer as a power or as a product of powers. $$ 3 y^{2} \cdot(2 y)^{3} $$

Rewrite the expression with positive exponents. $$(3 x y)^{-2}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{2 x^{3} y^{4}}{3 x y}\right)^{3} $$

Evaluate the expression. $$c^{3}+6 c d \text { when } c=2 \text { and } d=1$$

Evaluate the expression. $$3 y^{4}+15 y \text { when } y=-0.02$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \frac{8 \times 10^{-3}}{5 \times 10^{-5}} $$

Write your answer as a power or as a product of powers. $$ (-a b)\left(a^{2} b\right)^{2} $$

Rewrite the expression with positive exponents. $$\left(6 a^{-3}\right)^{3}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{16 x^{3} y}{-4 x y^{3}} \cdot-\frac{2 x y}{-x^{-1}} $$

Evaluate the expression. $$b^{2}-4 a c \text { when } a=1, b=3, \text { and } c=5$$

Evaluate the expression. $$(1-x)^{t} \text { when } x=0.5 \text { and } t=3$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \frac{1.4 \times 10^{-1}}{3.5 \times 10^{-4}} $$

Write your answer as a power or as a product of powers. $$ (-r s)\left(r s^{3}\right)^{2} $$

Rewrite the expression with positive exponents $$\frac{8}{m^{-2}}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{4 x^{3} y^{3}}{2 x y} \cdot \frac{5 x y^{2}}{2 y} $$

Evaluate the expression. $$\frac{a^{2}-b^{2}}{2 c^{2}}+9 \text { when } a=-3, b=5, \text { and } c=-2$$

Evaluate the expression. $$\frac{(1-x)^{t}}{2} \text { when } x=0.09 \text { and } t=2$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \frac{6.6 \times 10^{-1}}{1.1 \times 10^{-1}} $$

Write your answer as a power or as a product of powers. $$ (-2 x y)^{3}\left(-x^{2}\right) $$

Rewrite the expression with positive exponents $$\frac{1}{(4 x)^{-5}}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{36 a^{8} b^{2}}{a b} \cdot\left(\frac{6}{a b^{2}}\right)^{-1} $$

Solve the equation. Round the result to the nearest tenth if necessary. $$12 m-9=5 m-2$$

You are in charge of bringing breakfast for your scout troop. You buy 6 bagels and 8 donuts for a total of \(4.10. Then you decide to buy 3 extra of each for a total of \)1.80. How much did each bagel and donut cost?

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(3.0 \times 10^{-3}\right)^{2} $$

Write your answer as a power or as a product of powers. $$ (-3 c d)^{3}\left(-d^{2}\right) $$

Rewrite the expression with positive exponents $$\left(\frac{-4 x^{2}}{2 x^{-1}}\right)^{-1}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{16 x^{5} y^{-8}}{x^{7} y^{4}} \cdot\left(\frac{x^{3} y^{2}}{8 x y}\right)^{4} $$

Solve the equation. Round the result to the nearest tenth if necessary. $$5(2 x+2.3)-11.2=6 x-5$$

Solve the equation. $$-2(7-5 x)=10$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(9 \times 10^{3}\right)^{2} $$

Write your answer as a power or as a product of powers. $$ \left(5 b^{2}\right)^{3}\left(\frac{1}{2} b^{3}\right)^{2} $$

Simplify the expression. The simplified expression should have no negative exponents. $$ \frac{6 x^{-2} y^{2}}{x y^{-3}} \cdot \frac{\left(4 x^{2} y\right)^{-2}}{x y^{2}} $$

Solve the equation. Round the result to the nearest tenth if necessary. $$-1.3 y+3.7=4.2-5.4 y$$

Solve the equation. $$25-(6 x+5)=4(3 x-5)+4$$