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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)

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To simplify the expression \( \frac{\sqrt{49}}{7^{-3}} \), we can first rewrite the square root and use the properties of exponents.

  1. Simplifying the Square Root: \[ \sqrt{49} = 7 \]

  2. Substituting Back into the Expression: \[ \frac{7}{7^{-3}} \]

  3. Using the Quotient Property of Exponents: The Quotient Property states that \( \frac{a^m}{a^n} = a^{m-n} \). In this case: \[ \frac{7^1}{7^{-3}} = 7^{1 - (-3)} = 7^{1 + 3} = 7^4 \]

Now, we have simplified \( \frac{\sqrt{49}}{7^{-3}} \) to \( 7^4 \).

Next, if you want to express \( 7^4 \) with a rational exponent:

  1. Using the Negative Exponent Property: The expression \( 7^4 \) can also be expressed with a rational exponent, which would still be \( 7^4 \) because \( 4 \) is already a rational number.

Therefore, the equivalent expression for \( \frac{\sqrt{49}}{7^{-3}} \) is: \[ 7^4 \]

And the rational exponent for the new expression is \( 4 \).