Question

Which expression is equivalent to (4h⁷k²)⁴
Answer= 256gh²⁸k⁸

Answer 1

For this case we have that by definition of power properties we have to:

`(a ^ n) ^ m = a ^ {n * m}`

In addition, we know that:

`4 ^ 4 = 4 * 4 * 4 * 4 = 256`

We have the following expression:

`(4 * h ^ 7 * k ^ 2) ^ 4 =\\4 ^ {1 * 4} * h ^ {7 * 4} * k ^ {2} 4} =\\4 ^ 4 * h ^ {28} k ^ {8} =\\256 * h ^ {28} * k ^ {8}`

Answer:

`256 * h ^ {28} * k ^ {8}`