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Q19.

Expert-verifiedFound in: Page 404

Book edition
Student Edition

Author(s)
Carter, Cuevas, Day, Holiday, Luchin

Pages
801 pages

ISBN
9780078884801

**Simplify the expression **

**$\left(-2{g}^{3}h\right){\left(-3g{j}^{4}\right)}^{2}{\left(-ghj\right)}^{2}$**

The simplified version of $\left(-2{g}^{3}h\right){\left(-3g{j}^{4}\right)}^{2}{\left(-ghj\right)}^{2}$ is $-18{g}^{7}{h}^{3}{j}^{10}$.

According to this law, when a product is raised to a power, every factor of the product is raised to the power.

In general: ${\left(xy\right)}^{m}={x}^{m}{y}^{m}$

If a term with a power is itself raised to a power then the powers are multiplied together.

In general: ${\left({x}^{m}\right)}^{n}={x}^{m\times n}$

If the two terms have the same base (in this case *x*) and are to be multiplied together, then their indices are added.

** **

In general: ${x}^{m}\times {x}^{n}={x}^{m+n}$

The given expression is: $\left(-2{g}^{3}h\right){\left(-3g{j}^{4}\right)}^{2}{\left(-ghj\right)}^{2}$

** **

Apply the laws of indices and simplify.

$\left(-2{g}^{3}h\right){\left(-3g{j}^{4}\right)}^{2}{\left(-ghj\right)}^{2}=\left(-2{g}^{3}h\right)\left[{\left(-3\right)}^{2}{\left(g\right)}^{2}{\left({j}^{4}\right)}^{2}\right]\left[{\left(-g\right)}^{2}{\left(h\right)}^{2}{\left(j\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left(-2{g}^{3}h\right)\left[9{g}^{2}\left({j}^{4\times 2}\right)\right]\left({g}^{2}{h}^{2}{j}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(-2{g}^{3}h\right)\left[9{g}^{2}\left({j}^{8}\right)\right]\left({g}^{2}{h}^{2}{j}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(-2{g}^{3}h\right)\left(9{g}^{2}{j}^{8}\right)\left({g}^{2}{h}^{2}{j}^{2}\right)$

Collect the like terms together and use multiplication rule to simplify further.

$\left(-2{g}^{3}h\right){\left(-3g{j}^{4}\right)}^{2}{\left(-ghj\right)}^{2}=\left(-2{g}^{3}h\right)\left(9{g}^{2}{j}^{8}\right)\left({g}^{2}{h}^{2}{j}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(-2\times 9\right)\left({g}^{3}\times {g}^{2}\times {g}^{2}\right)\left(h\times {h}^{2}\right)\left({j}^{8}\times {j}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(-18\right)\left({g}^{3+2+2}\right)\left({h}^{1+2}\right)\left({j}^{8+2}\right)\phantom{\rule{0ex}{0ex}}=-18{g}^{7}{h}^{3}{j}^{10}$

**Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.**

**At a family fun centre, the Wilson and Sanchez families each bought video game tokens and batting cage tokens as shown in the table.**

Family | Wilson | Sanchez |

Number of Video Game Tokens | 25 | 30 |

Number of Batting Cage Tokens | 8 | 6 |

Total Cost | $\mathrm{\$}26.50$ | $\mathrm{\$}25.50$ |

**What is the cost in dollars of a batting cage token at the family fun centre?**

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