Single-Variable Algebra

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GED Math › Single-Variable Algebra

Questions 1 - 10

Simplify:

$\left (2x^{-4} \right )^{-2}$

$\frac{x^{8}}{4}$

$\frac{1}{4x^{8}}$

$\frac{x^{8}}{256}$

$\frac{1}{256x^{8}}$

Explanation

$\left (2x^{-4} \right )^{-2}$

$=\left ( \frac{2}{x^{4}} \right )^{-2}$

$=\left ( \frac{x^{4}}{2} \right )^{2}$

$= \frac{\left (x^{4}\right )^{2}}{2^{2}}$

$= \frac{ x^{4 \cdot 2} }{2^{2}}$

$= \frac{ x^{8} }{4}$

Simplify:

$\left (2x^{-4} \right )^{-2}$

$\frac{x^{8}}{4}$

$\frac{1}{4x^{8}}$

$\frac{x^{8}}{256}$

$\frac{1}{256x^{8}}$

Explanation

$\left (2x^{-4} \right )^{-2}$

$=\left ( \frac{2}{x^{4}} \right )^{-2}$

$=\left ( \frac{x^{4}}{2} \right )^{2}$

$= \frac{\left (x^{4}\right )^{2}}{2^{2}}$

$= \frac{ x^{4 \cdot 2} }{2^{2}}$

$= \frac{ x^{8} }{4}$

Simplify completely:

$\frac{3xy \cdot 7xy}{12y^{3}}$

$\frac{7 x^{2} }{4y }$

$\frac{7 x^{2}y }{4 }$

$\frac{7 x^{2} }{4y^{2} }$

$\frac{7 x }{4y^{2} }$

Explanation

$\frac{3xy \cdot 7xy}{12y^{3}}$

$= \frac{3 \cdot 7 \cdot x \cdot x \cdot y \cdot y}{12y^{3}}$

$= \frac{21 x^{2} y^{2} }{12y^{3}}$

$= \frac{21 x^{2} }{12y^{3-2}}$

$= \frac{21 x^{2} }{12y }$

$= \frac{21 x^{2} \div 3 }{12y \div 3}$

$= \frac{7 x^{2} }{4y }$

Timmy works at a fast food chain retail store five days a week, eight hours a day. Suppose it costs him $2.00 everyday to drive to and from work. He makes $10.00 per hour. How much will Timmy have at the end of the week, before applicable taxes?

$\$390$

$\$398$

$\$320$

$\$70$

$\$360$

Explanation

Timmy makes ten dollars per hour for eight hours.

$$10 \cdot 8 = $80$

For five days: $$80 \cdot 5 = $400$

Timmy also will pay $$2 \cdot 5 = $10$ for the week to get to work and back.

Subtract his expense from his earnings for the week.

$$400 -$10 = \$390$

Timmy will have $\$390$ by the end of the week.

Simplify completely:

$\frac{3xy \cdot 7xy}{12y^{3}}$

$\frac{7 x^{2} }{4y }$

$\frac{7 x^{2}y }{4 }$

$\frac{7 x^{2} }{4y^{2} }$

$\frac{7 x }{4y^{2} }$

Explanation

$\frac{3xy \cdot 7xy}{12y^{3}}$

$= \frac{3 \cdot 7 \cdot x \cdot x \cdot y \cdot y}{12y^{3}}$

$= \frac{21 x^{2} y^{2} }{12y^{3}}$

$= \frac{21 x^{2} }{12y^{3-2}}$

$= \frac{21 x^{2} }{12y }$

$= \frac{21 x^{2} \div 3 }{12y \div 3}$

$= \frac{7 x^{2} }{4y }$

$\$390$

$\$398$

$\$320$

$\$70$

$\$360$

Explanation

Timmy makes ten dollars per hour for eight hours.

$$10 \cdot 8 = $80$

For five days: $$80 \cdot 5 = $400$

Timmy also will pay $$2 \cdot 5 = $10$ for the week to get to work and back.

Subtract his expense from his earnings for the week.

$$400 -$10 = \$390$

Timmy will have $\$390$ by the end of the week.

Simplify:

$\left (\frac{3}{t} \right )^{3}$

$\frac{27}{t^{3}}$

$\frac{t^{3}}{27}$

$\frac{9}{t^{3}}$

$9}{t^{3}$

Explanation

Apply the power of a quotient rule:

$\left (\frac{3}{t} \right )^{3} = \frac{3^{3}}{t^{3}} = \frac{27}{t^{3}}$

Simplify:

$\left (\frac{3}{t} \right )^{3}$

$\frac{27}{t^{3}}$

$\frac{t^{3}}{27}$

$\frac{9}{t^{3}}$

$9}{t^{3}$

Explanation

Apply the power of a quotient rule:

$\left (\frac{3}{t} \right )^{3} = \frac{3^{3}}{t^{3}} = \frac{27}{t^{3}}$

Simplify:

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

$\frac{t^{3}}{125}$

$-\frac{125}{t^{3}}$

$\frac{t^{3}}{1 5}$

$-\frac{1 5}{t^{3}}$

Explanation

Raise a fraction to a negative power by raising its reciprocal to the power of the absolute value of the exponent. Then apply the power of a quotient rule:

$\left (\frac{5}{t} \right )^{-3} = \left (\frac{t}{5} \right )^{ 3} = \frac{t^{ 3}}{5^{ 3}} = \frac{t^{ 3}}{125}$

Simplify:

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

$\frac{t^{3}}{125}$

$-\frac{125}{t^{3}}$

$\frac{t^{3}}{1 5}$

$-\frac{1 5}{t^{3}}$

Explanation

Raise a fraction to a negative power by raising its reciprocal to the power of the absolute value of the exponent. Then apply the power of a quotient rule:

$\left (\frac{5}{t} \right )^{-3} = \left (\frac{t}{5} \right )^{ 3} = \frac{t^{ 3}}{5^{ 3}} = \frac{t^{ 3}}{125}$

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