Question

simplify the expression:
$\left(\frac{a}{b^{2}}\
ight)^{7}=\square$
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Explanation:

Step1: Apply power - of - a - quotient rule

The power - of - a - quotient rule states that \((\frac{x}{y})^n=\frac{x^n}{y^n}\). For the expression \((\frac{a}{b^{2}})^7\), we have \(x = a\), \(y=b^{2}\), and \(n = 7\). So, \((\frac{a}{b^{2}})^7=\frac{a^7}{(b^{2})^7}\).

Step2: Apply power - of - a - power rule

The power - of - a - power rule states that \((x^m)^n=x^{mn}\). For the term \((b^{2})^7\), where \(x = b\), \(m = 2\), and \(n = 7\), we get \((b^{2})^7=b^{2\times7}=b^{14}\).

Answer:

\(\frac{a^{7}}{b^{14}}\)