Question

simplify. express your answer using positive exponents.
$p^{-4}q^{-2}r^{0} \cdot pq^{0}r \cdot p^{0}q^{7}r^{0}$

Explanation:

Step1: Recall exponent rules

We use the rules \(a^m \cdot a^n = a^{m + n}\) and \(a^0=1\) (for \(a
eq0\)). Also, \(a^{-n}=\frac{1}{a^n}\) to convert negative exponents to positive.

First, handle the coefficients for each variable (\(p\), \(q\), \(r\)) separately.

Step2: Combine exponents for \(p\)

For the variable \(p\):
The terms are \(p^{-4}\), \(p^{1}\), \(p^{0}\)
Using \(a^m \cdot a^n=a^{m + n}\), we have \(p^{-4+1 + 0}=p^{-3}\)

Step3: Combine exponents for \(q\)

For the variable \(q\):
The terms are \(q^{-2}\), \(q^{0}\), \(q^{7}\)
Using the exponent rule, we get \(q^{-2 + 0+7}=q^{5}\)

Step4: Combine exponents for \(r\)

For the variable \(r\):
The terms are \(r^{0}\), \(r^{1}\), \(r^{0}\)
Using the rule, we have \(r^{0 + 1+0}=r^{1}=r\)

Step5: Convert negative exponents to positive

We have \(p^{-3}=\frac{1}{p^{3}}\)

Now, multiply all the simplified terms together:
\(p^{-3}\cdot q^{5}\cdot r=\frac{q^{5}r}{p^{3}}\)

Answer:

\(\dfrac{q^{5}r}{p^{3}}\)