Question

Evaluate the following:

`(64)^(-3/2)`

Answer 1

Given: `(64)^(-3/2)`

Step-wise calculation:

1. Write 64 as a power of 2:

64 = 2⁶

2. Substitute in the expression:

`(64)^(-3/2) = (2^6)^(-3/2)`

3. Use the power of a power property (a^m)ⁿ = a^{m × n}:

`(2^6)^(-3/2) = 2^(6 xx (-3/2))`

`(2^6)^(-3/2) = 2^-9`

4. Convert negative exponent to reciprocal:

`2^-9 = 1/2^9`

5. Calculate (2⁹):

2⁹ = 512

So, `(64)^(-3/2) = 1/(512)`.