Question

(1/64)^(2/3)


SOLVE LAW OF INDICES

Answer 1

Using the law of indices, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Now we need to simplify the denominator by finding the cube root of 64:

64^(1/3) = 4

Substituting this value in the original expression, we get:

(1/64)^(2/3) = (1^(2/3))/(4^2)

Simplifying further, we have:

(1/64)^(2/3) = 1/16

Explanation:

Answer 2

To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).

So, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.

Now, we have:

(1/64)^(2/3) = 1/(64^(2/3))

To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:

64^(2/3) = (64^(1/3))^2 = 4^2 = 16

So, substituting this back into the original expression, we have:

(1/64)^(2/3) = 1/16

Therefore, (1/64)^(2/3) simplifies to 1/16.

Explanation: