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When can I add exponents?

1 Answer

Apr 7, 2016

$x^{a} \times x^{b} = x^{a + b}$ $x^a xx x^b=x^(a+b)$

Explanation:

Exponents can be added when two of the same base are multiplied. That is, $x^{a} \times x^{b} = x^{a + b}$ $x^a xx x^b = x^(a+b)$ . For example:

$2^{3} \times 2^{5} = 2^{3 + 5} = 2^{8}$ $2^3xx2^5 = 2^(3+5)=2^8$
$5^{- 1} \times 5^{1} = 5^{- 1 + 1} = 5^{0} = 1$ $5^(-1)xx5^1 = 5^(-1+1) = 5^0 = 1$
$7^{\frac{1}{4}} \times 7^{\frac{3}{4}} = 7^{\frac{1}{4} + \frac{3}{4}} = 7^{1} = 7$ $7^(1/4)xx7^(3/4) = 7^(1/4+3/4) = 7^(1)=7$

Note that this does not apply when the bases are different.

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