Question

Multiply or divide as indicated. Leave your answer with no factors in the denominator. p⁻⁴q⁵r⁶/p⁻³qr⁻²

Answer 1

Answer:

$p^{-1}q^{4}r^{8}$.

Step-by-step explanation:

The given expression is $\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}$.

Recall and use the following rule of exponents;

$\frac{a^m}{a^n}=a^{m-n}$

We apply this rule to obtain:

$p^{-4--3}q^{5-1}r^{6--2}$

$p^{-4+3}q^{4}r^{6+2}$.

This simplifies to:

$p^{-1}q^{4}r^{8}$.

Since we do not want to leave any factor in the denominator, the required answer is:

$p^{-1}q^{4}r^{8}$.

Answer 2

Answer: $\frac{q^4r^8}{p}$

Step-by-step explanation:

By the Negative exponent rule, we know that:

$a^{-1}=\frac{1}{a}$

By the Quotient of powers property, we know that:

$\frac{a^m}{a^n}=a^{(m-n)$

And by the Product of powers property, we know that:

$(a^m)(a^n)=a^{(m+n)}$

Applying this properties, we get:

$\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}=\frac{p^3q^5r^6r^2}{p^4q}=\frac{q^4r^8}{p}$