Mathematics, 23.01.2020 18:31 isophk

Nadine and calvin are simplifying the expression (startfraction r superscript negative 5 baseline s superscript negative 3 baseline over r superscript 8 baseline s superscript negative 2 baseline endfraction) superscript negative 4. nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get startfraction r superscript negative 20 baseline s superscript negative 12 baseline over r superscript 32 baseline s superscript 8 baseline endfraction. calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r superscript negative 13 baseline s superscript negative 1 baseline) superscript negative 4. who is correct and why?

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Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step

That is $(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}$ Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step

Step-by-step explanation:

Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4

Their expression can be written as below

$(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}$

Nadine's first step is to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction

That is $\frac{r^{20}s^{12}}{r^{-32}s^8}$

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4

That is $r^{-13}s^{-1}$

Now simplify the given expression to check whose step is correct:

$(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}$

$=(r^{-5}s^{-3}r^{-8}s^{2})^{-4}$ ( using the property $\frac{1}{a^m}=a^{-m}$ )

$=(r^{-5-8}s^{-3+2})^{-4}$

$=(r^{-13}s^{-1})^{-4}$

Therefore $(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}$

Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.

That is $(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}$ Calvin's step is the correct step .Because this is the correct way to do simplify the rational expression.And also because Nadine made a blender mistake in her operations in step

Answer from: alexialiles19

The correct answer is D or

Calvin is correct because he correctly applied the quotient of powers rule.

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if x decreases by 4 then y increases by 10

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