Question

In Exercise, evaluate each expression. 643/4

Answer 1

Answer:

$\\ 64^{\frac{3}{4}} = 16\sqrt{2}$

Step-by-step explanation:

We need here to remember that:

$\\{(x^{a})}^{b} = x^{a * b}$

$\\{x^{a} * x^{b} = x^{a + b}$

Then,

$\\ 64^{\frac{3}{4}} = {(8^{2})}^{(\frac{3}{4})} = {{(2^{3})}^{2}}^\frac{3}{4}$

$\\ 64^{\frac{3}{4}} = {{2^{3}}^2}^\frac{3}{4} = 2^\frac{3*2*3}{4}$

$\\ 64^{\frac{3}{4}} = 2^\frac{2*3*3}{4} = 2^\frac{3*3}{2} = 2^\frac{9}{2}$

$\\ 64^{\frac{3}{4}} = 2^{\frac{9}{2}}$

Since $\\ \frac{9}{2} = \frac{4}{2} + \frac{4}{2} + \frac{1}{2}$

$\\ 64^{\frac{3}{4}} = 2^{\frac{9}{2}} = {2^{(\frac{4}{2} + \frac{4}{2} + \frac{1}{2})}$

$\\ 64^{\frac{3}{4}} = 2^{\frac{4}{2}} * 2^{\frac{4}{2}} * {2}^{\frac{1}{2}$

$\\ 64^{\frac{3}{4}} = 2^{2} * 2^{2} * {2}^{\frac{1}{2}$

$\\ 64^{\frac{3}{4}} = 4 * 4 * \sqrt{2} = 16 \sqrt{2}$