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Use the Quotient Property and Negative Exponent Property to generate an equivalent expression for √49/7−^3

. What will the rational exponent be for the new expression?(1 point)
7^

1 answer

To simplify the expression \(\frac{\sqrt{49}}{7^{-3}}\) using the Quotient Property and the Negative Exponent Property, let's work through the steps:

  1. Simplify the square root: \(\sqrt{49} = 7\)

  2. Rewrite the expression: The expression now becomes \(\frac{7}{7^{-3}}\).

  3. Apply the Quotient Property: The Quotient Property states that \(\frac{a^m}{a^n} = a^{m-n}\). Applying this here: \[ \frac{7^1}{7^{-3}} = 7^{1 - (-3)} = 7^{1 + 3} = 7^4 \]

The equivalent expression is \(7^4\).

Thus, the rational exponent for the new expression is:

\[ \boxed{4} \]