How do you simplify ${(5 x^{6} y^{4})}^{2}$ $(5x ^ { 6} y ^ { 4} ) ^ { 2}$ ?

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How do you simplify ${(5 x^{6} y^{4})}^{2}$ $(5x ^ { 6} y ^ { 4} ) ^ { 2}$ ?

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Answer 1 · 2018-06-20T16:02:58

See a solution process below:

Explanation:

First, use this rule for exponents to rewrite the $5$ $5$ term.

$a = a^{1}$ $a = a^color(red)(1)$

${(5 x^{6} y^{4})}^{2} \Rightarrow {(5^{1} x^{6} y^{4})}^{2}$ $(5x^6y^4)^2 => (5^color(red)(1)x^6y^4)^2$

Now, use this rule for exponents to eliminate the outer exponent:

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

${(5^{1} x^{6} y^{4})}^{2} \Rightarrow 5^{1 \times 2} x^{6 \times 2} y^{4 \times 2} \Rightarrow 5^{2} x^{12} y^{8} \Rightarrow 25 x^{12} y^{8}$ $(5^color(red)(1)x^color(red)(6)y^color(red)(4))^color(blue)(2) => 5^(color(red)(1)xxcolor(blue)(2))x^(color(red)(6)xxcolor(blue)(2))y^(color(red)(4)xxcolor(blue)(2)) => 5^2x^12y^8 => 25x^12y^8$

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How do you simplify ${(5 x^{6} y^{4})}^{2}$ $(5x ^ { 6} y ^ { 4} ) ^ { 2}$ ?

1 Answer

Explanation:

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