Evaluate \(\frac{(81^{\frac{3}{4}}-27^{\frac{1}{3}})}{3 \times 2^3}\)
A
3
B
1
C
\(\frac{1}{3}\)
D
\(\frac{1}{8}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{81^{\frac{3}{4}}-27^{\frac{1}{3}}}{3 \times 2^3}\)
= \(\frac{(3^{3-\frac{3}{4}}-3^{3-\frac{3}{4}})}{3\times 2^3}\)
= \(\frac{3^3 - 3}{3 \times 8}\)
= \(\frac{27-3}{24}\\=\frac{24}{24}\) =1
Source: Myschool Past Questions Archive (Record #8221)