Review Exercises

$\mathrm{-6}{a}^4$

$n^3-3n^2+3n-1$

$5m+9$

$y^2+6y^3+9y^4$

$\mathrm{-8}{y}^3-5y^3$

Subtract $10x^2$ from $3x^2$

$(8m^2+12m-5)-(2m^2-7m-1)$

$(5u^2+8u)-(4u-7)$

Find the difference of $x^2+6x+8$ and $x^2-8x+15$

$200x-\frac{1}{5}{x}^2$ when $x=0$

$5+40x-\frac{1}{2}{x}^2$ when $x=10$

$5+40x-\frac{1}{2}{x}^2$ when $x=0$

The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160}{x}^2+\frac{1}{2}x.$ Find the fuel efficiency when $x=20$ mph.

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

$-3^2$

$2·2^6$

$x·x^8$

${(r^3)}^2$

${(a^{10})}^y$

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

${(\mathrm{-10}mnp)}^4$

${(4y)}^2(8y)$

${(5s{t}^2)}^3{(2s^3{t}^4)}^2$

$\left(\frac{1}{3}{c}^2\right)\left(30c^8\right)$

$\left(\frac{2}{3}{m}^3{n}^6\right)\left(\frac{1}{6}{m}^4{n}^4\right)$

$a^2(a^2-9a-36)$

$(4n-5)(2n^3)$

$(y-4)(y+12)$

$(6p-11)(3p-10)$

$(k+6)(k-9)$

$(2y-9)(5y-7)$

$(x-8)(x+9)$

$(10a-1)(3a-3)$

$(5b-2)(3b^2+b-9)$

$(4y-1)(6y^2-12y+5)$

$\frac{a^6}{a}$

$\frac{x}{x^5}$

$y^0$

$12a^0-15b^0$

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

${\left(\frac{s}{10t}\right)}^2$

$\frac{u^3}{u^2·u^4}$

${\left(\frac{p^4·p^5}{p^3}\right)}^2$

${\left(\frac{5s^2}{4t}\right)}^3$

$\mathrm{-26}{a}^8÷\left(2a^2\right)$

$\frac{\mathrm{-30}{x}^8}{\mathrm{-36}{x}^9}$

$\frac{11u^6{v}^3}{55u^2{v}^8}$

$\frac{42r^2{s}^4}{6r{s}^3}-\frac{54r{s}^2}{9s}$

${\left(\mathrm{-10}\right)}^{\mathrm{-3}}$

${\left(8n\right)}^{\mathrm{-1}}$

$r^{\mathrm{-5}}·r^{\mathrm{-4}}$

${\left(m^5\right)}^{\mathrm{-1}}$

$\frac{q^4}{q^{20}}$

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

$0.00814$

According to www.cleanair.com, U.S. businesses use about $\mathrm{21,000,000}$ tons of paper per year.

$1.5\times {10}^8$

$9.413\times {10}^{\mathrm{-5}}$

$\left(1.5\times {10}^{\mathrm{-3}}\right)\left(4.8\times {10}^{\mathrm{-1}}\right)$

$\frac{9\times {10}^{\mathrm{-3}}}{1\times {10}^{\mathrm{-6}}}$

$8a,72$

$9y^4,21y^5,15y^6$

$15r+35$

$10c^2-10c$

$\mathrm{-7}{x}^8-28x^3$

$2q^5-16q^3+30q^2$