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

Answer:

Option B.

Step-by-step explanation:

The given expression is

$\dfrac{28p^9q^{-5}}{12p^{-6}q^{7}}, p\neq 0, q\neq 0$

It can be rewritten as

$\dfrac{28}{12}\cdot \dfrac{p^9}{p^{-6}}\cdot \dfrac{q^{-5}}{q^{7}}$

Using properties of exponents, we get

$\dfrac{7}{3}\cdot p^{9}p^{6}\cdot \dfrac{1}{q^{7}q^{5}}$     $[\because a^{-n}=\dfrac{1}{a^n}]$

$\dfrac{7}{3}\cdot p^{9+6}\cdot \dfrac{1}{q^{7+5}}$        $[\because a^ma^n=a^{m+n}]$

$\dfrac{7}{3}\cdot p^{15}\cdot \dfrac{1}{q^{12}}$

$\dfrac{7p^{15}}{3q^{12}}$

Therefore, the correct option is B.

Answer 2

Answer:

b

Step-by-step explanation: