Question

1 which property of exponents must be applied when simplifying the expression \\(\frac{3^{9}}{3^{-6}}\\)? a power rule b product rule c zero exponent property d quotient rule

Explanation:

To simplify \(\frac{3^{9}}{3^{-6}}\), we recall the properties of exponents. The Quotient Rule for exponents states that \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (where \(a
eq0\), \(m\) and \(n\) are real numbers). Here, we have a quotient of two powers with the same base (\(a = 3\), \(m=9\), \(n=- 6\)), so the Quotient Rule is applied. The Power Rule is for \((a^{m})^{n}=a^{mn}\), the Product Rule is for \(a^{m}\cdot a^{n}=a^{m + n}\), and the Zero Exponent Property is for \(a^{0}=1\) (\(a
eq0\)), none of which apply here.

Answer:

D. Quotient Rule