Review Exercises

ⓐ $a^2-b^2$
ⓑ $24d^3$
ⓒ $x^2+8x-10$
ⓓ $m^2{n}^2-2mn+6$
ⓔ $7y^3+y^2-2y-4$

$\mathrm{-14}k+19k$

$\mathrm{-9}c-18c$

$3m^2+7n^2-3m^2$

$\text{13a}+b$

$(9p^2-5p+3)+(4p^2-4)$

$(7y^2-8y)-(y-4)$

Find the sum of $\left(a^2+6a+9\right)\text{and}\left(5a^3-7\right)$

Evaluate $10-12x$ when:

1. ⓐ $x=3$
2. ⓑ $x=0$
3. ⓒ $x=\mathrm{-1}$

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $\mathrm{-4}{p}^2+460p.$ Find the revenue received when $p=75$ dollars.

${17}^1$

${\left(0.5\right)}^3$

$\text{−}{2}^6$

$p^{15}·p^{16}$

$8·8^5$

$y^c·y^3$

${(5^3)}^2$

${\left(3^r\right)}^s$

${\left(\mathrm{-5}y\right)}^3$

${\left(10xyz\right)}^3$

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

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

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

$(\mathrm{-9}{n}^7)(\mathrm{-16}n)$

$\left(\frac{5}{9}a{b}^2\right)\left(27a{b}^3\right)$

$\mathrm{-4}(y+13)$

$p(p+3)$

$\mathrm{-6}u(2u+7)$

$3q^2(q^2-7q+6)$ 3

$(b-4)·11$

$\left(6y-7\right)\left(2y-5\right)$

$(y-4)(y-8)$

$(q+16)(q-3)$

$(u^2+6)(u^2-5)$

$(8mn+3)(2mn-1)$

$\left(3x-4\right)\left(6x^2+x-10\right)$

$(7m+1)(m^2-10m-3)$

${\left(q-15\right)}^2$

${(8u+1)}^2$

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

$\left(y+\frac{2}{5}\right)\left(y-\frac{2}{5}\right)$

$(6-r)(6+r)$

$(5p^4-4q^3)(5p^4+4q^3)$

$(6a+11)(6a-11)$

${(c^4+9d)}^2$

$(a^2+4b)(4a-b^2)$

$\frac{{10}^{25}}{{10}^5}$

$\frac{v^{12}}{v^{48}}$

$\frac{5}{5^8}$

$x^0$

$\left(\text{−}{12}^0\right)$ ${\left(\mathrm{-12}\right)}^0$

${\left(25x\right)}^0$

${\left(19n\right)}^0-{\left(25m\right)}^0$

${\left(\frac{m}{3}\right)}^4$

${\left(\frac{x}{2y}\right)}^6$

$\frac{n^{10}}{{\left(n^5\right)}^2}$

${\left(\frac{r^8}{r^3}\right)}^4$

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

$\frac{{\left(3n^2\right)}^4{\left(\mathrm{-5}{n}^4\right)}^3}{{\left(\mathrm{-2}{n}^5\right)}^2}$

$\frac{64a^5{b}^9}{\mathrm{-16}{a}^{10}{b}^3}$

$\frac{\left(8p^6{q}^2\right)\left(9p^3{q}^5\right)}{16p^8{q}^7}$

$\left(35x^2-75x\right)÷5x$

$\frac{550p^6-300p^4}{10p^3}$

$\frac{96a^5{b}^2-48a^4{b}^3-56a^2{b}^4}{8a{b}^2}$

$\frac{105y^5+50y^3-5y}{5y^3}$

$\left(v^2-16v+64\right)÷\left(v-8\right)$

$\left(n^2-3n-14\right)÷\left(n+3\right)$

$\left(u^3-8\right)÷\left(u-2\right)$

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

${\left(6u\right)}^{\mathrm{-3}}$

${\left(\frac{3}{4}\right)}^{\mathrm{-2}}$

$q^{\mathrm{-6}}·q^{\mathrm{-5}}$

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

$\frac{a^8}{a^{12}}$

$\frac{r^{\mathrm{-2}}}{r^{\mathrm{-3}}}$

0.00429

In 2015, the population of the world was about 7,200,000,000 people.

$1.5\times {10}^{10}$

$5.5\times {10}^{\mathrm{-1}}$

$\left(3.5\times {10}^{\mathrm{-2}}\right)\left(6.2\times {10}^{\mathrm{-1}}\right)$

$\frac{9\times {10}^{\mathrm{-5}}}{3\times {10}^2}$