Question

Can you multiply constants with the same variable exponents? `2^x(10^x+6^x)`

How would you distribute the `2^x` in `2^x(10^x+6^x)`

Answer 1

`2^x(10^x+6^x) = 20^x+12^x`

Explanation:

If `a, b > 0` then:

`a^x * b^x = (ab)^x`

Hence we find:

`2^x(10^x+6^x) = (2^x * 10^x) + (2^x * 6^x) = 20^x+12^x`

Footnote

The rule:

`a^x * b^x = (ab)^x`

does not work if `a, b < 0` and `x` is allowed to take non-integer values.

For example:

`-1 = (-1)^(1/2) * (-1)^(1/2) != ((-1)*(-1))^(1/2) = 1^(1/2) = 1`