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Simplify the expressions for the following problems.
( [link] ) $\frac{-3\left\{\left[\left(-2-3\right)\right]\left[-2\right]\right\}}{-3\left(4-2\right)}$
5
( [link] ) If $z=\frac{x-u}{s}$ , find $z$ if $x=14$ , $u=20$ , and $s=2$ .
$-3$
When simplifying the terms for the following problems, write each so that only positive exponents appear.
( [link] ) $\frac{5{x}^{3}{y}^{-2}}{{z}^{-4}}$
$\frac{5{x}^{3}{z}^{4}}{{y}^{2}}$
( [link] ) ${2}^{-2}{m}^{6}{(n-4)}^{-3}$
$\frac{{m}^{6}}{4{\left(n-4\right)}^{3}}$
( [link] ) $\frac{{6}^{-1}{x}^{3}{y}^{-5}{x}^{-3}}{{y}^{-5}}$
$\frac{1}{6}$
( [link] ) $\frac{{(k-6)}^{2}{(k-6)}^{-4}}{{(k-6)}^{3}}$
$\frac{1}{{\left(k-6\right)}^{5}}$
( [link] ) $\frac{{(y+1)}^{3}{(y-3)}^{4}}{{(y+1)}^{5}{(y-3)}^{-8}}$
$\frac{{\left(y-3\right)}^{12}}{{\left(y+1\right)}^{2}}$
( [link] ) $\frac{({3}^{-6})({3}^{2})({3}^{-10})}{({3}^{-5})({3}^{-9})}$
1
( [link] ) ${\left[\frac{{r}^{6}{s}^{-2}}{{m}^{-5}{n}^{4}}\right]}^{-4}$
$\frac{{n}^{16}{s}^{8}}{{m}^{20}{r}^{24}}$
( [link] ) $\begin{array}{cc}{({c}^{0})}^{-2},& c\ne 0\end{array}$
1
( [link] ) Write $0.000271$ using scientific notation.
$2.71\times {10}^{-4}$
( [link] ) Write $8.90\times {10}^{5}$ in standard form.
$890,000$
( [link] ) Find the value of $(3\times {10}^{5})(2\times {10}^{-2})$ .
$6000$
( [link] ) Find the value of ${(4\times {10}^{-16})}^{2}$ .
$1.6\times {10}^{-31}$
( [link] ) If $k$ is a negative integer, is $-k$ a positive or negative integer?
a positive integer
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