Question

simplify the expression. assume that the denominator does not equal zero. write any variables in alphabetical order. \\(\frac{p^{4}t^{-3}}{r^{-2}}\\)

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^n}\) and \(\frac{1}{a^{-n}} = a^n\). So we can rewrite the denominator \(r^{-2}\) using this rule.
\(\frac{p^{4}t^{-3}}{r^{-2}}=p^{4}t^{-3}\times r^{2}\)

Step2: Rewrite \(t^{-3}\) using negative exponent rule

Using \(a^{-n}=\frac{1}{a^n}\), we can rewrite \(t^{-3}\) as \(\frac{1}{t^{3}}\). So now the expression becomes:
\(p^{4}\times\frac{1}{t^{3}}\times r^{2}\)

Step3: Rearrange the variables in alphabetical order

Rearranging the terms with variables in alphabetical order (\(p\), \(r\), \(t\)) and combining the constants (there are no constants here other than the coefficients of the variables which are 1 for each variable term), we get:
\(\frac{p^{4}r^{2}}{t^{3}}\)

Answer:

\(\frac{p^{4}r^{2}}{t^{3}}\)