Question

The numerator is 49 under a square root and the denominator is a 7 with an exponent of -3. If you use the Quotient Property and Negative Exponent Property, how do you generate an equivalent expression for that number.

Answer 1

To simplify the expression \(\frac{\sqrt{49}}{7^{-3}}\), you can use the Quotient Property and the Negative Exponent Property. Let's break it down step by step:

1. **Evaluate the numerator**:
\[
\sqrt{49} = 7
\]

2. **Rewrite the denominator using the Negative Exponent Property**:
\[
7^{-3} = \frac{1}{7^3}
\]

3. **Rewriting the entire expression**:
\[
\frac{7}{7^{-3}} = 7 \cdot 7^3
\]

4. **Using the Quotient Property of exponents**:
Remember that \(a^{-n} = \frac{1}{a^n}\):
\[
7 \cdot 7^3 = 7^{1 + 3} = 7^4
\]

Thus, the expression \(\frac{\sqrt{49}}{7^{-3}}\) simplifies to:
\[
7^4
\]

If you want to express this as a number, you can compute \(7^4\):
\[
7^4 = 2401
\]

So the equivalent expression for \(\frac{\sqrt{49}}{7^{-3}}\) is \(7^4\) or numerical value \(2401\).