Question

simplify.
\frac{(3b^{3})^{3}}{(5b^{7})^{2}}
write your answer using only po

Explanation:

Step1: Apply power of a product rule

For \((3b^3)^3\), we have \(3^3\times(b^3)^3 = 27b^{9}\) (using \((ab)^n=a^n b^n\) and \((a^m)^n=a^{mn}\)).
For \((5b^7)^2\), we have \(5^2\times(b^7)^2=25b^{14}\) (using the same rules).
So the expression becomes \(\frac{27b^{9}}{25b^{14}}\).

Step2: Apply quotient rule for exponents

Using \(\frac{a^m}{a^n}=a^{m - n}\) for the variable part, we get \(\frac{27}{25}\times b^{9-14}=\frac{27}{25}b^{-5}\).

Answer:

\(\frac{27}{25}b^{-5}\)