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For the following problems, simplify each of the expressions.
( [link] ) $\frac{{1}^{8}+{4}^{0}+{3}^{3}(1+4)}{{2}^{2}(2+15)}$
$\frac{137}{68}$
( [link] ) $\frac{2\cdot {3}^{4}-{10}^{2}}{4-3}+\frac{5({2}^{2}+{3}^{2})}{11-6}$
75
(
[link] ) Write the appropriate relation symbol
$(>,<)$ in place of the
$*$ .
$5(2+11)\ast 2(8-3)-2$
$>$
For the following problems, use algebraic notation.
( [link] ) $(x-1)$ times $(3x\text{\hspace{0.17em}}\text{plus}\text{\hspace{0.17em}}2)$ .
$\left(x-1\right)\left(3x+2\right)$
( [link] ) A number divided by twelve is less than or equal to the same number plus four.
$\frac{x}{12}\le \left(x+4\right)$
(
[link] ) Locate the approximate position of
$-1.6$ on the number line.
( [link] ) Is 0 a positive number, a negative number, neither, or both?
Zero is neither positive nor negative.
( [link] ) Draw a portion of the number line and place points at all even integers strictly between 14 and 20.
( [link] ) Draw a portion of the number line and place points at all real numbers strictly greater than $-1$ but less than or equal to 4.
( [link] ) What whole numbers can replace $x$ so that the following statement is true? $-4\le x\le 5$ .
$0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}3,\text{\hspace{0.17em}}4,\text{\hspace{0.17em}}5$
( [link] ) Is there a largest real number between and including 6 and 10? If so, what is it?
yes; 10
( [link] ) Use the commutative property of multiplication to write $m(a+3)$ in an equivalent form.
$\left(a+3\right)m$
( [link] ) Use the commutative properties to simplify $3a4b8cd$ .
$96abcd$
( [link] ) Use the commutative properties to simplify $4(x-9)2y(x-9)3y$ .
$24{y}^{2}{\left(x-9\right)}^{2}$
( [link] ) Simplify 4 squared times $x$ cubed times $y$ to the fifth.
$16{x}^{3}{y}^{5}$
( [link] ) Simplify $(3)(3)(3)aabbbbabba(3)a$ .
$81{a}^{5}{b}^{6}$
For the following problems, use the rules of exponents to simplify each of the expressions.
$72{a}^{11}{b}^{7}$
${x}^{8}{y}^{7}$
( [link] , [link] ) $\frac{52{x}^{7}{y}^{10}{(y-{x}^{4})}^{12}{(y+x)}^{5}}{4{y}^{6}{(y-{x}^{4})}^{10}(y+x)}$
$13{x}^{7}{y}^{4}{\left(y-{x}^{4}\right)}^{2}{\left(y+x\right)}^{4}$
${x}^{4n}{y}^{12m}{z}^{8p}$
$\frac{{x}^{\nabla}{x}^{\square}{y}^{\Delta}}{{x}^{\Delta}{y}^{\nabla}}$
( [link] , [link] ) What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?
a variable
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