Question 1

In Exercise, evaluate each expression.
643/4

Question 2

Answer:

$\\ 64^{(3)/(4)} = 16√(2)$

Explanation:

We need here to remember that:

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

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

Then,

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

$\\ 64^{(3)/(4)} = {{2^(3)}^2}^(3)/(4) = 2^(3*2*3)/(4)$

$\\ 64^{(3)/(4)} = 2^(2*3*3)/(4) = 2^(3*3)/(2) = 2^(9)/(2)$

$\\ 64^{(3)/(4)} = 2^{(9)/(2)}$

Since
$\\ (9)/(2) = (4)/(2) + (4)/(2) + (1)/(2)$

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

$\\ 64^{(3)/(4)} = 2^{(4)/(2)} * 2^{(4)/(2)} * {2}^{(1)/(2)$

$\\ 64^{(3)/(4)} = 2^(2) * 2^(2) * {2}^{(1)/(2)$

$\\ 64^{(3)/(4)} = 4 * 4 * √(2) = 16 √(2)$

Please log in or register to add a comment.

Please log in or register to answer this question.