Question

Simplify the expression.
a)1/64
b)2^-30
c)64
d)2^30

Answer 1

`\left(((-1)^5)/((-2)^(-3)) \right)^2\\\\\\=\left((-1)/((1)/((-2)^3)) \right)^2\\\\\\=\left(-1 * -8\right)^2\\\\=8^2\\\\=64`

Answer 2

`\huge\boxed{\bf\:64}`

Explanation:

`\left(((-1)^(5))/(\left(-2\right)^(-3))\right)^(2)`

Now, simplify
`(-1)^(5) = -1`. Then,

`\left((-1)/(\left(-2\right)^(-3))\right)^(2)`

Calculate:
`(-2)^(-3) = (1)/((-2)^(3)) = - (1)/(8)`.

`\left((-1)/(-(1)/(8))\right)^(2)`

Divide
`-1` by
`- (1)/(8)`. The result will be
`8.`

`\left(-\left(-8\right)\right)^(2) \\= 8^(2)`

Calculate
`8` to its square which is
`64.`

`8^(2)\\=\boxed{\bf\: 64} \: \:\mathrm{(3^(rd) \: option)}`

`\rule{150pt}{2pt}`