Use the quotient property and negative exponent property to generate an equivalent expression for square root 49/7^-3

Answer 1

To simplify the expression \(\sqrt{\frac{49}{7^{-3}}}\) using the quotient property and the negative exponent property, we can follow these steps:

1. Apply the quotient inside the square root: \[ \sqrt{\frac{49}{7^{-3}}} = \sqrt{49} \div \sqrt{7^{-3}} \]

2. Simplify \(\sqrt{49}\): \[ \sqrt{49} = 7 \]

3. Simplify \(\sqrt{7^{-3}}\) using the property of square roots and negative exponents: \[ \sqrt{7^{-3}} = 7^{-3/2} \]

4. Now, divide the two results: \[ 7 \div 7^{-3/2} = 7^{1 - (-3/2)} = 7^{1 + 3/2} = 7^{1 + 1.5} = 7^{2.5} = 7^{5/2} \]

Thus, the expression \(\sqrt{\frac{49}{7^{-3}}}\) simplifies to: \[ 7^{5/2} \]

So, the equivalent expression for \(\sqrt{\frac{49}{7^{-3}}}\) is: \[ 7^{5/2} \]