Question

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

Answer 1

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`