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sattari [20]
3 years ago
14

This is really confusing me: Simplify so that your answers contain only positive exponents.

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
3 0

Answer:

  see below

Step-by-step explanation:

For simplifying expressions of this sort, there are four rules of exponents that come into play;

  a^ba^c=a^{b+c}\\\\(ab)^c=a^cb^c\\\\(a^b)^c=a^{bc}\\\\\dfrac{1}{a^b}=a^{-b}\ \quad\text{which means}\quad a^b=\dfrac{1}{a^{-b}}

__

I find it convenient to eliminate the fractions by adding the exponents, then rewrite any negative exponents as denominator factors.

23. \quad\dfrac{1}{x^{-2}}=x^2\\\\24. \quad\dfrac{mn}{m^2n^3}=m^{1-2}n^{1-3}=m^{-1}n^{-2}=\dfrac{1}{mn^2}\\\\25. \quad\dfrac{k^{-2}}{k^{-3}}=k^{-2-(-3)}=k\\\\26. \quad\left(\dfrac{m^2}{n^3}\right)^3=\dfrac{m^{2\cdot 3}}{n^{3\cdot 3}}=\dfrac{m^6}{n^9}\\\\27. \quad\dfrac{x^2y^3z^4}{x^{-3}y^{-4}z^{-5}}=x^{2-(-3)}y^{3-(-4)}z^{4-(-5)}=x^5y^7z^9

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Negative exponents mean that the base is on the wrong side of the fraction line. For example, x^-2 is the same as 1/x^2. In this example, 1/2^-2 would be 2.

2/1^2 = 2
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3 years ago
The quotient of 6 divided by the difference of m minus 3<br>A.15<br>B.2<br>C.3<br>D.21<br>E.42​
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2 years ago
Given the equation 3x-3=6x+1, select the reasoning that correctly solves for x . Add 3 subtract 6x then divide by 3 or subtract
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To correctly solve x from the given equation,
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Simplifying,
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7 0
3 years ago
A proofreader earns $8.50 for each page that he proofreads. If he works 7.5 hours and proofreads 14 pages each day on average, w
dimulka [17.4K]

Answer:

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Step-by-step explanation:

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this means that for every hour the proofreader is working he proof reads 1.8666667 pages since he makes 8.5 for every page we have to multiply the pages per hour times the salary of every page to get his average hourly wage

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0.125 × 100 = 12.5

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3 years ago
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