Question

Simplify the equation. (2³)⁻²

Answer 1

Let's simplify the following expression:

`(2^3)^(-2)`

Step 1:

`\mathrm{Apply\: exponent\: rule}\colon\quad \mleft(a^b\mright)^c=a^(bc),\: \quad \: a\ge0`
`\mleft(2^3\mright)^(-2)=2^(3\mleft(-2\mright))`
`=2^{\mleft\{-6\mright\}}`

Step 2:

`\mathrm{Apply\: exponent\: rule}\colon\quad \: a^(-b)=(1)/(a^b)`
`2^(-6)=(1)/(2^6)`
`=(1)/(64)`

Therefore, the answer is 1/64