When you multiply two numbers with exponents, should you add, subtract, multiply or divide the exponents?

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When you multiply two numbers with exponents, should you add, subtract, multiply or divide the exponents?

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Answer 1 · 2016-04-08T05:12:36

Please see below

Explanation:

When we multiply two numbers with exponents, we add exponents only when they have common base.

As an example, when we multiply say $48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^{3} \times 3^{1}$ $48=2xx2xx2xx2xx3=2^3xx3^1$ with $36 = 2 \times 2 \times 3 \times 3 = 2^{2} \times 3^{2}$ $36=2xx2xx3xx3=2^2xx3^2$ , then

$48 \times 36 = (2^{3} \times 3^{1}) \times (2^{2} \times 3^{2}) = 2^{3 + 2} \times 3^{1 + 2} = 2^{5} \times 3^{3}$ $48xx36=(2^3xx3^1)xx(2^2xx3^2)=2^(3+2)xx3^(1+2)=2^5xx3^3$

Similarly, when we divide two numbers with exponents, we should subtract the exponent of denominator from that of numerator provided they have common base.

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When you multiply two numbers with exponents, should you add, subtract, multiply or divide the exponents?

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