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

1 Answer
smendyka
Jun 20, 2018

See a solution process below:

Explanation:

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

#a = a^color(red)(1)#

#(5x^6y^4)^2 => (5^color(red)(1)x^6y^4)^2#

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

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(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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