지수법칙

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

Multiply Monomials

In the following exercises, multiply the following monomials.

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

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 $5\%$ 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 $\char36 40,000$, his salary after $1$ year was $\char36 40,000(1.05),$ after $2$ years was $\char36 40,000{(1.05)}^{2},$ after $3$ years was $\char36 40,000{(1.05)}^{3},$ 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.