Question

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?

Answer 1

The correct answer is D or

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

Explanation:

I just took the quiz

Answer 2

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
`((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

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

`((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
`(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:

`((r^(-5)s^(-3))/(r^8s^(-2)))^(-4)`

`=(r^(-5)s^(-3)r^(-8)s^(2))^(-4)` ( using the property
`(1)/(a^m)=a^(-m)` )

`=(r^(-5-8)s^(-3+2))^(-4)`

`=(r^(-13)s^(-1))^(-4)`

Therefore
`((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
`((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