Simplify 125\(^{−\frac{1}{3}}\) \times 49\(^{−\frac{1}{2}}\) \times 10\(^0\)
A
\(\frac{1}{35}\)
B
\(\frac{1}{350}\)
C
350
D
35
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Given: 125\(^{−\frac{1}{3}}\) \times 49\(^{−\frac{1}{2}}\) \times 10\(^0\)
125\(^{-1/3}\) = (5\(^3\))\(^{-1/3}\) = 5\(^{-1}\) = \(\frac{1}{5}\).
49\(^{-1/2}\) = (7\(^2\))\(^{-1/2}\) = 7\(^{-1}\) = \(\frac{1}{7}\).
10\(^0\) = 1.
Product = \(\frac{1}{5}\) x \(\frac{1}{7}\) x 1 = \(\frac{1}{35}\).
Source: Myschool Past Questions Archive (Record #74095)