Simplify the expressions using the quotient to a power property.
${\left(\frac{p}{q}\right)}^7$

• A. $\frac{p^7}{q}$
• B. $\frac{p}{q^7}$
• C. $\frac{p^7}{q^7}$
• D. $\frac{p}{q}$

Answer: (C)

Verified step by step guidance

1. Identify the given expression: \(\left(\frac{p}{q}\right)^7\).
2. Recall the quotient to a power property, which states that \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\), where \(a\) and \(b\) are any expressions and \(n\) is a positive integer.
3. Apply this property to the given expression by raising both the numerator and the denominator to the seventh power separately.
4. Rewrite the expression as \(\frac{p^7}{q^7}\).
5. This is the simplified form of the original expression using the quotient to a power property.