Home > Algebra > Exponential Properties Involving Products

How do you simplify #(6x^2)^4#?

Answer 1

Abigail Allen

See a solution process below:

First, use this rule of exponents to rewrite the term within the parenthesis:

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

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

Now, use this rule of exponents to simplify the expression:

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

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

#6^(color(red)(1) xx color(blue)(4))x^(color(red)(2) xx color(blue)(4)) =>#

#6^4x^8 =>#

#1296x^8#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Alexander

To simplify (6x^2)^4, raise each term within the parentheses to the fourth power:

(6x^2)^4 = 6^4 * (x^2)^4

= 1296 * x^8

By signing up, you agree to our Terms of Service and Privacy Policy

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.