Question

1. How do you multiply powers with the same base?

2. How do you divide powers with the same base?

3. How do you find the power of a power?

4. Simplify. (x^2*x^4)^3
____________.
x^8

Answer 1

Explanation:

`(1) \: {a}^(m) * {a}^(n) = {a}^(m + n) \\ \\ (2) \: \frac{ {a}^(m) }{{a}^(n)} = {a}^(m - n) \\ \\ (3) \: ({a}^(m )) ^(n) = {{a}^(m * n )} \\ \\ (4) \: \frac{ ( {x}^(2) * {x}^(4) )^(3)}{} \\ \\ = \frac{( {x}^(2 + 4) )^(3) }{ {x}^(8) } \\ \\ = \frac{( {x}^(6) )^(3) }{ {x}^(8) } \\ \\ = \frac{{x}^(6 * 3) }{ {x}^(8)} \\ \\ = {x}^(18 - 8) \\ \\ = {x}^(10)`