Question

5.1 exponent propertie
(1 point)
simplify the expression:
$(\frac{a}{b^{3}})^{6}=$
you have attempted this problem 0 times.
you have unlimited attempts remaining.

Explanation:

Step1: Apply the power - of - a - quotient rule

The power - of - a - quotient rule states that \((\frac{x}{y})^n=\frac{x^n}{y^n}\), where \(x = a\), \(y = b^3\), and \(n = 6\).
So, \((\frac{a}{b^3})^6=\frac{a^6}{(b^3)^6}\).

Step2: Apply the power - of - a - power rule

The power - of - a - power rule states that \((x^m)^n=x^{m\times n}\).
For \((b^3)^6\), we have \(m = 3\) and \(n = 6\), so \((b^3)^6=b^{3\times6}=b^{18}\).

Answer:

\(\frac{a^6}{b^{18}}\)