Question

Simplify the following:

`((x^(2a + 3))^5)/((x^(a + 1))^3`

Answer 1

Given: `((x^(2a + 3))^5)/((x^(a + 1))^3`

Stepwise calculation:

1. Apply the power of a power rule:

(x^m)ⁿ = x^mn 

`x^(5(2a + 3))/(x^(3(a + 1))) = (x^(10a + 15))/(x^(3a + 3))`

2. Apply the division rule for exponents with the same base:

`x^m/x^n = x^(m - n)`

`x^((10a + 15) - (3a + 3)) = x^(10a + 15 - 3a - 3)`

`x^((10a + 15) - (3a + 3)) = x^(7a + 12)`