12. Simplify the expression 7*−4⋅7*3/49√

Question

(2 points)
The simplified expression is
(do not include negative exponents) (Answer should be a simplified fraction)

Answer 1

To simplify the expression \(7^{-4} \cdot 7^{3} \div 49^{\frac{1}{2}}\), we can follow these steps:

1. Combine the powers of 7: \[ 7^{-4} \cdot 7^{3} = 7^{-4 + 3} = 7^{-1} \]

2. Simplify \(49^{\frac{1}{2}}\): Since \(49 = 7^2\), we have: \[ 49^{\frac{1}{2}} = (7^2)^{\frac{1}{2}} = 7^{2 \cdot \frac{1}{2}} = 7^{1} = 7 \]

3. Now we can write the expression as: \[ 7^{-1} \div 7 = 7^{-1} \cdot 7^{-1} = 7^{-1 - 1} = 7^{-2} \]

4. Convert back from negative exponent: \[ 7^{-2} = \frac{1}{7^2} = \frac{1}{49} \]

The simplified expression is: \[ \frac{1}{49} \]