Question 88

$$(16)^{\frac{-3}{4}}+2^{-3}+(8)^{\frac{-2}{3}}$$ is equivalent to

Solution

Expression : $$(16)^{\frac{-3}{4}}+2^{-3}+(8)^{\frac{-2}{3}}$$

= $$(2)^{4 \times \frac{-3}{4}} + \frac{1}{8} + (2)^{3 \times \frac{-2}{3}}$$

= $$(2)^{-3} + \frac{1}{8} + (2)^{-2}$$

= $$\frac{1}{8} + \frac{1}{8} + \frac{1}{4}$$

= $$\frac{1 + 2 + 1}{8} = \frac{4}{8}$$

= $$\frac{1}{2}$$

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