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 $7^{-4}\cdot 7^3÷{49}^{\frac{1}{2}}$, 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: $$7^{-1}÷7=7^{-1}\cdot 7^{-1}=7^{-1-1}=7^{-2}$$

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

The simplified expression is: $$\frac{1}{49}$$