Question

Which expression is equivalent to StartFraction 28 p Superscript 9 Baseline q Superscript negative 5 Baseline Over 12 p Superscript negative 6 Baseline q Superscript 7 Baseline EndFraction? Assume p not-equals 0, q not-equals 0.

StartFraction 2 Over p Superscript 15 Baseline q Superscript 12 Baseline EndFraction
StartFraction 7 p Superscript 15 Baseline Over 3 q Superscript 12 Baseline EndFraction
StartFraction 2 q Superscript 12 Baseline Over p Superscript 15 Baseline EndFraction
StartFraction 7 p Superscript 15 Baseline q Superscript 12 Baseline Over 3 EndFraction

Answer 1

b

Explanation:

Answer 2

Option B.

Explanation:

The given expression is

`(28p^9q^(-5))/(12p^(-6)q^(7)), p\\eq 0, q\\eq 0`

It can be rewritten as

`(28)/(12)\cdot (p^9)/(p^(-6))\cdot (q^(-5))/(q^(7))`

Using properties of exponents, we get

`(7)/(3)\cdot p^(9)p^(6)\cdot (1)/(q^(7)q^(5))`
`[\because a^(-n)=(1)/(a^n)]`

`(7)/(3)\cdot p^(9+6)\cdot (1)/(q^(7+5))`
`[\because a^ma^n=a^(m+n)]`

`(7)/(3)\cdot p^(15)\cdot (1)/(q^(12))`

`(7p^(15))/(3q^(12))`

Therefore, the correct option is B.