How do you multiply (5x ^ { 3} ) ^ { 2} \cdot ( 4x )^3?

1 Answer
Apr 7, 2017

See the entire solution process below:

Explanation:

First, use these two rules of exponents to eliminate the out exponents:

a = a^color(red)(1) and (x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))

(5x^3)^2 * (4x)^3 = (5^color(red)(1)x^color(red)(3))^color(blue)(2) * (4^color(red)(1)x^color(red)(1))^color(blue)(3) =

(5^(color(red)(1) xx color(blue)(2))x^(color(red)(3) xx color(blue)(2))) * (4^(color(red)(1) xx color(blue)(3))x^(color(red)(1) xx color(blue)(3))) = (5^2x^6) * (4^3x^3) = (25x^6) * (64x^3)

Next, rewrite the expression as:

(25x^6) * (64x^3) = (25 * 64)(x^6 * x^3) = 1600(x^6 * x^3)

Now, use this rule of exponents to complete the multiplication:

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

1600(x^6 * x^3) = 1600(x^color(red)(6) xx x^color(blue)(3)) = 1600x^(color(red)(6) + color(blue)(3)) = 1600x^9