How do you simplify ${(e^{3})}^{2} e^{2}$ $(e ^ { 3} ) ^ { 2} e ^ { 2}$ ?

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Answer 1 · 2017-02-24T20:13:35

See the entire simplification process below:

First, use this rule of exponents to simplify the term in parenthesis:

${(x^{a})}^{b} = x^{a \times b}$ $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

${(e^{3})}^{2} e = e^{3 \times 2} e = e^{6} e$ $(e^color(red)(3))^color(blue)(2)e = e^(color(red)(3) xx color(blue)(2))e = e^6e$

Now, we can use these two rule of exponents to complete the simplification:

$a = a^{1}$ $a = a^color(blue)(1)$ and $x^{a} \times x^{b} = x^{a + b}$ $x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))$

$e^{6} e = e^{6} e^{1} = e^{6 + 1} = e^{7}$ $e^color(red)(6)e = e^color(red)(6)e^color(blue)(1) = e^(color(red)(6) + color(blue)(1)) = e^7$

How do you simplify (e ^ { 3} ) ^ { 2} e ^ { 2}(e3)2e2(e ^ { 3} ) ^ { 2} e ^ { 2}?