10.2 Use multiplication properties of exponents  (Page 3/3)

$4^5$

${10}^3$

${\left(\frac{1}{2}\right)}^2$

${\left(\frac{3}{5}\right)}^2$

${(0.2)}^3$

${(0.4)}^3$

${(\mathrm{-5})}^4$

${(\mathrm{-3})}^5$

${\mathrm{-5}}^4$

${\mathrm{-3}}^5$

${\mathrm{-10}}^4$

${\mathrm{-2}}^6$

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

${\left(-\frac{1}{4}\right)}^4$

$-{0.5}^2$

$-{0.1}^4$

$x^3·x^6$

$m^4·m^2$

$a·a^4$

$y^{12}·y$

$3^5·3^9$

$5^{10}·5^6$

$z·z^2·z^3$

$a·a^3·a^5$

$x^a·x^2$

$y^p·y^3$

$y^a·y^b$

$x^p·x^q$

${(u^4)}^2$

${(x^2)}^7$

${(y^5)}^4$

${(a^3)}^2$

${({10}^2)}^6$

${(2^8)}^3$

${(x^{15})}^6$

${(y^{12})}^8$

${(x^2)}^y$

${(y^3)}^x$

${(5^x)}^y$

${(7^a)}^b$

${(5a)}^2$

${(7x)}^2$

${(-6m)}^3$

${(-9n)}^3$

${(4rs)}^2$

${(5ab)}^3$

${(4xyz)}^4$

${(-5abc)}^3$

${(x^2)}^4·{(x^3)}^2$

${(y^4)}^3·{(y^5)}^2$

${(a^2)}^6·{(a^3)}^8$

${(b^7)}^5·{(b^2)}^6$

${(3x)}^2(5x)$

${(2y)}^3(6y)$

${(5a)}^2{(2a)}^3$

${(4b)}^2{(3b)}^3$

${(2m^6)}^3$

${(3y^2)}^4$

${(10x^{2}y)}^3$

${(2m{n}^4)}^5$

${(\mathrm{-2}{a}^3{b}^2)}^4$

${(\mathrm{-10}{u}^2{v}^4)}^3$

${\left(\frac{2}{3}{x}^{2}y\right)}^3$

${\left(\frac{7}{9}p{q}^4\right)}^2$

${(8a^3)}^2{(2a)}^4$

${(5r^2)}^3{(3r)}^2$

${(10p^4)}^3{(5p^6)}^2$

${(4x^3)}^3{(2x^5)}^4$

${\left(\frac{1}{2}{x}^2{y}^3\right)}^4{(4x^5{y}^3)}^2$

${\left(\frac{1}{3}{m}^3{n}^2\right)}^4{(9m^8{n}^3)}^2$

${(3m^{2}n)}^2{(2m{n}^5)}^4$

${(2p{q}^4)}^3{(5p^{6}q)}^2$

$(12x^2)(\mathrm{-5}{x}^4)$

$(\mathrm{-10}{y}^3)(7y^2)$

$(\mathrm{-8}{u}^6)(\mathrm{-9}u)$

$(\mathrm{-6}{c}^4)(\mathrm{-12}c)$

$\left(\frac{1}{5}{r}^8\right)(20r^3)$

$\left(\frac{1}{4}{a}^5\right)(36a^2)$

$(4a^{3}b)(9a^2{b}^6)$

$(6m^4{n}^3)(7m{n}^5)$

$\left(\frac{4}{7}x{y}^2\right)(14x{y}^3)$

$\left(\frac{5}{8}{u}^{3}v\right)(24u^{5}v)$

$\left(\frac{2}{3}{x}^{2}y\right)\left(\frac{3}{4}x{y}^2\right)$

$\left(\frac{3}{5}{m}^3{n}^2\right)\left(\frac{5}{9}{m}^2{n}^3\right)$

Email Janet emails a joke to six of her friends and tells them to forward it to six of their friends, who forward it to six of their friends, and so on. The number of people who receive the email on the second round is $6^2,$ on the third round is $6^3,$ as shown in the table. How many people will receive the email on the eighth round? Simplify the expression to show the number of people who receive the email.

Salary Raul’s boss gives him a $\text{5\%}$ raise every year on his birthday. This means that each year, Raul’s salary is $1.05$ times his last year’s salary. If his original salary was $\text{\$40,000}$ , his salary after $1$ year was $\text{\$40,000}(1.05),$ after $2$ years was $\text{\$40,000}{(1.05)}^2,$ after $3$ years was $\text{\$40,000}{(1.05)}^3,$ as shown in the table below. What will Raul’s salary be after $10$ years? Simplify the expression, to show Raul’s salary in dollars.

Use the Product Property for Exponents to explain why $x·x=x^2.$

Explain why ${\mathrm{-5}}^3={(\mathrm{-5})}^3$ but ${\mathrm{-5}}^4\ne {(\mathrm{-5})}^4.$