Question

Find $\left(\frac{1}{2}\right)^{8} \cdot \left(\frac{3}{4}\right)^{-3}$.

Answer 1

The value of
`\(\left((1)/(2)\right)^(8) \cdot \left((3)/(4)\right)^(-3)\)` is
`\[ (64)/(6912) \]`.

To find the value of
`\(\left((1)/(2)\right)^(8) \cdot \left((3)/(4)\right)^(-3)\)`, you can simplify each term separately and then multiply them together.

1. Simplify
`\(\left((1)/(2)\right)^(8)\)`:

`\[ \left((1)/(2)\right)^(8) = (1)/(2^(8)) = (1)/(256) \]`

2. Simplify
`\(\left((3)/(4)\right)^(-3)\)`:

`\[ \left((3)/(4)\right)^(-3) = (1)/(\left((3)/(4)\right)^(3)) = (1)/((27)/(64)) = (64)/(27) \]`

Now, multiply the simplified terms:

`\[ (1)/(256) \cdot (64)/(27) \]`

To multiply fractions, multiply the numerators together and the denominators together:

`\[ (1 \cdot 64)/(256 \cdot 27) \]`

Simplify the fraction:

`\[ (64)/(6912) \]`

So,
`\(\left((1)/(2)\right)^(8) \cdot \left((3)/(4)\right)^(-3) = (64)/(6912) \)`.

the probable question may be: "Find the value of:
`\(\left((1)/(2)\right)^(8) \cdot \left((3)/(4)\right)^(-3)\)`"