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Sonja [21]
3 years ago
12

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

Mathematics
1 answer:
nika2105 [10]3 years ago
8 0

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}

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