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

Answer 1

Hazel Anglin

See a solution process below:

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, eliminate the outer exponent by applying this exponent rule:

#(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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Answer 2

Genesis Allen

To simplify (5x^6y^4)^2, you need to raise each term inside the parentheses to the power of 2. This gives you 5^2 * (x^6)^2 * (y^4)^2. Simplifying further, you get 25 * x^12 * y^8. Therefore, the simplified expression is 25x^12y^8.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.