Simplify x^a(1+x^b)

$x^{a} (1 + x^{b})$

Apply the distributive property.

$x^{a} \cdot 1 + x^{a} x^{b}$

Multiply $x^{a}$ by $1$ .

$x^{a} + x^{a} x^{b}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{a} + x^{a + b}$