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BaLLatris [955]
2 years ago
6

Simplify the expression. Assume that all variables represent nonzero real numbers.StartFraction (4 n Superscript 4 Baseline q Su

perscript 5 )squared (8 n Superscript 4 Baseline q )Superscript negative 2 Over (negative 3 nq Superscript 9 )Superscript negative 1 Baseline (4 n cubed q Superscript 9 )cubed EndFraction StartFraction
Mathematics
1 answer:
Alja [10]2 years ago
4 0

Answer:

\frac{ - 3}{ 256  {q}^{10} {n}^{8}  }

Step by step explanation:

\frac{ {(4 {n}^{4} {q}^{5})}^{2}  {(8 {n}^{4} q)}^{-2} }{  {(- 3 {nq}^{9})}^{ - 1}   {(4 {n}^{3} {q}^{9})  }^{3} }

first we will change the terms with negative superscrips to the other side of the fraction

\frac{{(4 {n}^{4} {q}^{5})}^{2}{(- 3 {nq}^{9})}^{ 1}}{{(4 {n}^{3} {q}^{9})}^{3} {(8 {n}^{4} q)}^{2} }

then we will distribute the superscripts

\frac{ {4}^{2} {n}^{2 \times 4} {q}^{2 \times 5} (- 3) {nq}^{9}}{ {4 }^{3}{n}^{3 \times 3} {q}^{9 \times 3} {8 }^{2}{n}^{4 \times 2}  {q}^{2} }

\frac{ {4}^{2} {n}^{8} {q}^{10} (- 3) {nq}^{9}}{ {4 }^{3}{n}^{9} {q}^{27} {8 }^{2}{n}^{8}  {q}^{2} }

as when multiplying two powers that have the same base, we can add the exponents and, to divide podes with the same base, we can subtract the exponents

{4}^{2 - 3}  {q}^{10  + 9 - 2 - 27}  {n}^{8 + 1 - 8 - 9}  {8}^{ - 2}  { (- 3)}^{1}

{4}^{ - 1}  {q}^{ - 10}  {n}^{ - 8}  {8}^{ - 2}  { (- 3)}^{1}

then we will change again the terms with negative superscrips to the other side of the fraction

\frac{ - 3}{ 4 \times  {8}^{2}  {q}^{10} {n}^{8}  }

\frac{ - 3}{ 256  {q}^{10} {n}^{8}  }

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Answer:

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3) 44x + 6y + 3

4) 9m - 6n + 23

Step-by-step explanation:

1. Add like terms. 6a + 9a=15a. -8c - 7c=-15c

2. Add like terms. You can rearrange them in descending order based off of exponents and variables.

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4. Distribute the (-3) to what in the parentheses. It should end up being (-6n + 15 - 3m). Then you add like terms and put the expression in descending order.

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3 years ago
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A newly launched clothing line is rapidly increasing in popularity. Every month 20% more items of clothing are sold. If 70,800 i
prohojiy [21]

Answer:

<u>212,400 items</u> were sold in 10 months.

Step-by-step explanation:

Given:

Items sold this month = 70,800

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We need to find number of items sold in coming 10 months.

Solution:

First we will find number of items increase in each month.

number of items increase in each month can be calculated by Percent Increase in every month multiplied by Items sold this month and the divided by 100.

number of items increase in each month = \frac{20}{100} \times 70800 = 14,160

Now we will find number of item sold in 10 months.

number of item sold in 10 months is equal to sum of Items sold this month and number of items increase in each month multiplied by 10.

framing in equation form we get;

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3 years ago
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melamori03 [73]

Given rational expression is

-\frac{8x}{8x^2+2x}

Now we need to find the restricted values if any for this rational expression.

Restricted values means the possible values of the used variable (x) that will make denominator 0 as division by 0 is not defined.

So to find the restricted values, we just set denominator equal to 0 and solve for x

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Hence final answer is x=0, -1/4

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