Question

Evaluate (64^-1/2)^-2/3

Answer 1

Answer:

4

Step-by-step explanation:

We'll do two things here.  First remember that when a number is raised to an exponent, and the result is raised to another exponent, you can simply multiply those exponents and apply them to the base.  So we can multiply -1/2 and -2/3, giving us 1/3, which is what we'll raise 64 to.

The other thing to remember is that a fractional exponent is the same as a root of that base.  So raising a number to the power of 1/3 just means we want the cube root of that number.

Applying those and we get:

$(64^{-\frac{1}{2}})^{-\frac{2}{3}}\\= 64^{(-\frac{1}{2} \times -\frac{2}{3})}\\= 64^{\frac{1}{3}}\\= 4$