Evaluate \(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
A
27
B
1
C
\(\frac{1}{3}\)
D
\(\frac{1}{8}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
= \(\frac{(3^{4})^{\frac{3}{4}} - (3^{3})^{\frac{1}{3}}}{3 \times 2^{3}}\)
= \(\frac{3^{3} - 3^{1}}{24}\)
= \(\frac{27 - 3}{24} = 1\)
Source: Myschool Past Questions Archive (Record #30878)