Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
The value of $64^{-\frac{1}{3}}\Big(64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big)$ is:
A
1
B
13
C
-3
D
-2
✓
Answer
-3
Solution: Find the value of $64^{\frac {1}{3}}\Big(64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big)$ So, $\Rightarrow64^{\frac {1}{3}}\Big(64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big)=2^{6\times\frac{1}{3}}\Big(2^{6\times\frac{1}{3}}-2^{6\times\frac{2}{3}}\Big)$ $=2^{-2}(2^2-2^4)$ $=2^2(4-16)$ $\Rightarrow64^{\frac {1}{3}}\Big(64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big)=\frac{1}{2^2}\times-12$ $=\frac{1}{4}\times-12$ $=-3$ Hence the correct statement is c.
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