Question

\frac{15p^{7}}{(3p^{3})^{2}}

Explanation:

Step1: Simplify the denominator

First, we simplify the denominator \((3p^{3})^{2}\). Using the power of a product rule \((ab)^n = a^n b^n\) and the power of a power rule \((a^m)^n = a^{mn}\), we have:
\((3p^{3})^{2}=3^{2}\times(p^{3})^{2}=9p^{6}\)
So the expression becomes \(\frac{15p^{7}}{9p^{6}}\).

Step2: Simplify the fraction

We can simplify the fraction by dividing the coefficients and using the quotient rule for exponents \(a^m\div a^n=a^{m - n}\) (where \(a
eq0\) and \(m,n\) are real numbers).
First, simplify the coefficients: \(\frac{15}{9}=\frac{5}{3}\) (dividing numerator and denominator by 3).
Then, simplify the variable part: \(\frac{p^{7}}{p^{6}}=p^{7 - 6}=p\) (using the quotient rule for exponents).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part together: \(\frac{5}{3}\times p=\frac{5}{3}p\)

Answer:

\(\frac{5}{3}p\)