# 3.10 Proficiency exam

 Page 1 / 1
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.This module provides a proficiency exam for the chapter "Basic Operations with Real Numbers".

## Proficiency exam

Simplify the expressions for the following problems.

( [link] ) $-\left\{-\left[\left(-6\right)\right]\right\}$

$-6$

( [link] ) $-|-15|$

$-15$

( [link] ) $-{\left[|-12|-10\right]}^{2}$

$-4$

( [link] ) $-5\left(-6\right)+4\left(-8\right)-|-5|$

$-7$

( [link] ) $\frac{3\left(-8\right)-\left(-2\right)\left(-4-5\right)}{\left(-2\right)\left(-3\right)}$

$-7$

( [link] ) $-|7|-{\left(2\right)}^{2}+{\left(-2\right)}^{2}$

$-7$

( [link] ) $\frac{-6\left(2\right)\left(-2\right)}{-\left(-5-3\right)}$

3

( [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] ) $\frac{1}{-{\left(-5\right)}^{-3}}$

125

( [link] ) $\frac{5{x}^{3}{y}^{-2}}{{z}^{-4}}$

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

( [link] ) ${2}^{-2}{m}^{6}{\left(n-4\right)}^{-3}$

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

( [link] ) $4{a}^{-6}\left(2{a}^{-5}\right)$

$\frac{8}{{a}^{11}}$

( [link] ) $\frac{{6}^{-1}{x}^{3}{y}^{-5}{x}^{-3}}{{y}^{-5}}$

$\frac{1}{6}$

( [link] ) $\frac{{\left(k-6\right)}^{2}{\left(k-6\right)}^{-4}}{{\left(k-6\right)}^{3}}$

$\frac{1}{{\left(k-6\right)}^{5}}$

( [link] ) $\frac{{\left(y+1\right)}^{3}{\left(y-3\right)}^{4}}{{\left(y+1\right)}^{5}{\left(y-3\right)}^{-8}}$

$\frac{{\left(y-3\right)}^{12}}{{\left(y+1\right)}^{2}}$

( [link] ) $\frac{\left({3}^{-6}\right)\left({3}^{2}\right)\left({3}^{-10}\right)}{\left({3}^{-5}\right)\left({3}^{-9}\right)}$

1

( [link] ) ${\left({a}^{4}\right)}^{-3}$

$\frac{1}{{a}^{12}}$

( [link] ) ${\left[\frac{{r}^{6}{s}^{-2}}{{m}^{-5}{n}^{4}}\right]}^{-4}$

$\frac{{n}^{16}{s}^{8}}{{m}^{20}{r}^{24}}$

( [link] ) $\begin{array}{cc}{\left({c}^{0}\right)}^{-2},& c\ne 0\end{array}$

1

( [link] ) Write $0.000271$ using scientific notation.

$2.71×{10}^{-4}$

( [link] ) Write $8.90×{10}^{5}$ in standard form.

$890,000$

( [link] ) Find the value of $\left(3×{10}^{5}\right)\left(2×{10}^{-2}\right)$ .

$6000$

( [link] ) Find the value of ${\left(4×{10}^{-16}\right)}^{2}$ .

$1.6×{10}^{-31}$

( [link] ) If $k$ is a negative integer, is $-k$ a positive or negative integer?

a positive integer