3.6 Negative exponents

$x^{-4}{y}^7$

$\frac{a^2}{b^{-4}}$

$\frac{x^3{y}^4}{z^{-8}}$

$\frac{6m^{-3}{n}^{-2}}{7k^{-1}}$

$\frac{1}{a^{-2}{b}^{-6}{c}^{-8}}$

$\frac{3a{(a-5b)}^{-2}}{5b{(a-4b)}^5}$

Rewrite $\frac{36x^8{b}^3}{3^2{x}^{-2}{b}^{-5}}$ in a simpler form.

Write $\frac{2^4{m}^{-3}{n}^7}{4^{-1}{x}^5}$ in a simpler form and one in which no denominator appears.

Find the value of $\frac{2}{5^{-2}}+6^{-2}\cdot 2^3\cdot 3^2$ .

$x^{-2}$

$x^{-4}$

$x^{-7}$

$a^{-8}$

$a^{-10}$

$b^{-12}$

$b^{-14}$

$y^{-1}$

$y^{-5}$

${(x+1)}^{-2}$

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

${(y-4)}^{-6}$

${(a+9)}^{-10}$

${(r+3)}^{-8}$

${(a-1)}^{-12}$

$x^3{y}^{-2}$

$x^7{y}^{-5}$

$a^4{b}^{-1}$

$a^7{b}^{-8}$

$a^2{b}^3{c}^{-2}$

$x^3{y}^2{z}^{-6}$

$x^3{y}^{-4}{z}^{2}w$

$a^7{b}^{-9}z{w}^3$

$a^3{b}^{-1}z{w}^2$

$x^5{y}^{-5}{z}^{-2}$

$x^4{y}^{-8}{z}^{-3}{w}^{-4}$

$a^{-4}{b}^{-6}{c}^{-1}{d}^4$

$x^9{y}^{-6}{z}^{-1}{w}^{-5}{r}^{-2}$

$4x^{-6}{y}^2$

$5x^2{y}^2{z}^{-5}$

$7a^{-2}{b}^2{c}^2$

$4x^3{(x+1)}^2{y}^{-4}{z}^{-1}$

$7a^2{(a-4)}^3{b}^{-6}{c}^{-7}$

$18b^{-6}{(b^2-3)}^{-5}{c}^{-4}{d}^5{e}^{-1}$

$7{(w+2)}^{-2}{(w+1)}^3$

$2{(a-8)}^{-3}{(a-2)}^5$

${(x^2+3)}^3{(x^2-1)}^{-4}$

${(x^4+2x-1)}^{-6}{(x+5)}^4$

${(3x^2-4x-8)}^{-9}{(2x+11)}^{-3}$

${(5y^2+8y-6)}^{-2}{(6y-1)}^{-7}$

$7a{(a^2-4)}^{-2}{(b^2-1)}^{-2}$

${(x-5)}^{-4}3b^2{c}^4{(x+6)}^8$

${(y^3+1)}^{-1}5y^3{z}^{-4}{w}^{-2}{(y^3-1)}^{-2}$

$5x^3(2x^{-7})$

$3y^{-3}(9x)$

$6a^{-4}(2a^{-6})$

$4a^2{b}^2{a}^{-5}{b}^{-2}$

$5^{-1}{a}^{-2}{b}^{-6}{b}^{-11}{c}^{-3}{c}^9$

$2^3{x}^2{2}^{-3}{x}^{-2}$

$7a^{-3}{b}^{-9}\cdot 5a{}^{6}b{c}^{-2}{c}^4$

${(x+5)}^2{(x+5)}^{-6}$

${(a-4)}^3{(a-4)}^{-10}$

$8{(b+2)}^{-8}{(b+2)}^{-4}{(b+2)}^3$

$3a^5{b}^{-7}{(a^2+4)}^{-3}6a^{-4}b{(a^2+4)}^{-1}(a^2+4)$

$-4a^3{b}^{-5}(2a^2{b}^7{c}^{-2})$

$-2x^{-2}{y}^{-4}{z}^4(-6x^3{y}^{-3}z)$

${(-5)}^2{(-5)}^{-1}$

${(-9)}^{-3}{(9)}^3$

${(-1)}^{-1}{(-1)}^{-1}$

${(4)}^2{(2)}^{-4}$

$\frac{1}{a^{-4}}$

$\frac{1}{a^{-1}}$

$\frac{4}{x^{-6}}$

$\frac{7}{x^{-8}}$

$\frac{23}{y^{-1}}$

$\frac{6}{a^2{b}^{-4}}$

$\frac{3c^5}{a^3{b}^{-3}}$

$\frac{16a^{-2}{b}^{-6}c}{2y{z}^{-5}{w}^{-4}}$

$\frac{24y^2{z}^{-8}}{6a^2{b}^{-1}{c}^{-9}{d}^3}$

$\frac{3^{-1}{b}^5{(b+7)}^{-4}}{9^{-1}{a}^{-4}{(a+7)}^2}$

$\frac{36a^6{b}^5{c}^8}{3^2{a}^3{b}^7{c}^9}$

$\frac{45a^4{b}^2{c}^6}{15a^2{b}^7{c}^8}$

$\frac{3^3{x}^4{y}^{3}z}{3^{2}x{y}^5{z}^5}$

$\frac{21x^2{y}^2{z}^5{w}^4}{7xy{z}^{12}{w}^{14}}$

$\frac{33a^{-4}{b}^{-7}}{11a^3{b}^{-2}}$

$\frac{51x^{-5}{y}^{-3}}{3xy}$

$\frac{2^6{x}^{-5}{y}^{-2}{a}^{-7}{b}^5}{2^{-1}{x}^{-4}{y}^{-2}{b}^6}$

$\frac{{(x+3)}^3{(y-6)}^4}{{(x+3)}^5{(y-6)}^{-8}}$

$\frac{4x^3}{y^7}$

$\frac{5x^4{y}^3}{a^3}$

$\frac{23a^4{b}^5{c}^{-2}}{x^{-6}{y}^5}$

$\frac{2^3{b}^5{c}^2{d}^{-9}}{4b^{4}cx}$

$\frac{10x^3{y}^{-7}}{3x^5{z}^2}$

$\frac{3x^2{y}^{-2}(x-5)}{9^{-1}{(x+5)}^3}$

$\frac{14a^2{b}^2{c}^{-12}{(a^2+21)}^{-4}}{4^{-2}{a}^2{b}^{-1}{(a+6)}^3}$

$4^{-1}$

$7^{-1}$

$6^{-2}$

$2^{-5}$

$3^{-4}$

$6\cdot 3^{-3}$

$4\cdot 9^{-2}$

$28\cdot {14}^{-1}$

$2^{-3}(3^{-2})$

$2^{-1}\cdot 3^{-1}\cdot 4^{-1}$

${10}^{-2}+3({10}^{-2})$

${(-3)}^{-2}$

${(-10)}^{-1}$

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

$\frac{4^{-1}}{5^{-2}}$

$\frac{2^4-7}{4^{-1}}$

$\frac{2^{-1}+4^{-1}}{2^{-2}+4^{-2}}$

$\frac{{21}^0-2^6}{2\cdot 6-13}$

${(a^6)}^{-2}$

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

${(x^7)}^{-4}$

${(x^4)}^{-8}$

${(b^{-2})}^7$

${(b^{-4})}^{-1}$

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

${(y^{-9})}^{-3}$

${(a^{-1})}^{-1}$

${(b^{-1})}^{-1}$

$\begin{array}{ll}{(a^0)}^{-1},\hfill & a\ne 0\hfill \end{array}$

$\begin{array}{ll}{(m^0)}^{-1},\hfill & m\ne 0\hfill \end{array}$

${(x^{-3}{y}^7)}^{-4}$

${(x^6{y}^6{z}^{-1})}^2$

${(a^{-5}{b}^{-1}{c}^0)}^6$

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

${\left(\frac{a^{-8}}{b^{-6}}\right)}^3$

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

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

${\left(\frac{5^{-1}{a}^3{b}^{-6}}{x^{-2}{y}^9}\right)}^2$

${\left(\frac{4m^{-3}{n}^6}{2m^{-5}n}\right)}^3$

${\left(\frac{r^5{s}^{-4}}{m^{-8}{n}^7}\right)}^{-4}$

${\left(\frac{h^{-2}{j}^{-6}}{k^{-4}p}\right)}^{-5}$

( [link] ) Simplify ${(4x^5{y}^3{z}^0)}^3$

( [link] ) Find the sum. $-15+3$ .

( [link] ) Find the difference. $8-(-12)$ .

( [link] ) Simplify $(-3)(-8)+4(-5)$ .

( [link] ) Find the value of $m$ if $m=\frac{-3k-5t}{kt+6}$ when $k=4$ and $t=-2$ .