Question

Question 1) When multiplying powers with the same base, keep the base and _______________ the exponents.

Answer 1

The rules are

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

$\dfrac{x^a}{x^b} = x^{a-b}$

Let me show you why with a couple of examples: suppose we want to multiply

$4^3\cdot 4^2$

Since powers are just repeated multiplications, we have

$4^3\cdot 4^2 = \underbrace{4\cdot 4\cdot 4}_{4^3}\cdot\underbrace{4\cdot 4}_{4^2}=4^5 = 4^{3+2}$

Similarly, we have

$\dfrac{4^3}{4^2} = \dfrac{4\cdot 4 \cdot 4}{4\cdot 4} = 4 = 4^1 = 4^{3-2}$