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PtichkaEL [24]
3 years ago
9

Which expression is equivalent to a^m divide a^n?(20points)

Mathematics
1 answer:
Citrus2011 [14]3 years ago
6 0
<h3><u>Answer</u> :</h3>

\bigstar\:\boxed{\bf{\dfrac{a^m}{a^n}=a^{m-n}}}

<h3><u>Learn More</u> :</h3>

\dag\sf\:\:a^m\times a^n=a^{m+n}

\dag\sf\:\:\dfrac{a^m}{a^n}=a^{m-n}=\dfrac{1}{a^{n-m}}

\dag\sf\:\:a^{-m}=\dfrac{1}{a^m}

\dag\sf\:\:(a^{m})^n=a^{mn}

\dag\sf\:\:a^1=a

\dag\sf\:\:a^0=1

\dag\sf\:\:\sqrt[n]{a^m}=a^{\frac{m}{n}}

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<u>Part 1)</u> Use the fact that there are 12 inches in a foot

a) How many inches tall is a 7 foot basketball player?

we know that

1 foot=12 inches

so by proportion

\frac{12}{1} \frac{inches}{foot} =\frac{x}{7} \frac{inches}{feet} \\ \\x=12*7\\ \\x=84\ inches

therefore

<u>the answer Part 1a) is</u>

84\ inches

Part b) If a yard is a 3 feet long, how many inches are in a yard?

we know that

1 yard=3 feet

1 foot=12 inches

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Convert 3 feet to inches

by proportion

\frac{12}{1} \frac{inches}{foot} =\frac{x}{3} \frac{inches}{feet} \\ \\x=12*3\\ \\x=36\ inches    

therefore

<u>the answer Part 1b) is</u>

36\ inches

<u>Part 2) </u>At the farmer's market two pounds of peaches cost $4.20 How much will five pounds cost?

by proportion

\frac{4.20}{2} \frac{\$}{pounds} =\frac{x}{5} \frac{\$}{pounds} \\ \\2*x=4.2*5\\ \\x=4.2*5/2=\$10.5    

therefore

<u>the answer Part 2) is</u>

\$10.5

<u>Part 3) </u>Janice mother gave her a ten dollars bill to buy five pounds each of bananas and apples at the grocery store. When she got there she found that bananas were 80 c per pound and apples were $1.40 per pound.

Did Janice's mother give her enough money? If so, should she receive any change? If not, how much more money does she need?

 we know that

<u>Find the cost of the bananas</u>

5\ pounds*0.80\frac{\$}{pounds}=\$4

<u>Find the cost of the apples</u>

5\ pounds*1.40\frac{\$}{pounds}=\$7

Sum the cost of the bananas and the cost of the apples

\$4+\$7=\$11

\$11 > \$10------> Janice's mother didn't give her enough money

She needs more money

She needs-------> \$11-\$10=\$1

therefore

<u>the answer part 3) is</u>

She needs  \$1 more


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Solve each system using substitution:<br> 1. 4x - 5y= -15<br> y= -3x + 22
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Plug in your y= equation into the y variable in the other equation

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            ^^
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Then, divide the whole equation by 19

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y = -3 (5) + 22
y = -15 + 22
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<em><u>x = 5</u></em>
<em><u>y = 7</u></em>
<em><u>(5, 7)</u></em>
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Answer:

Step-by-step explanation:

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3 years ago
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