Question

How do you multiply `(2^ { 2} \cdot 3^ { 2} ) ^ { 3}`?

Answer 1

See some solution processes below:

Explanation:

First process:

Square and the multiply each term within the parenthesis and then cube the result:

`(2^2 * 3^2)^3 = (4 * 9)^3 = 36^3 = 46,656`

Another method is to use this rule for exponents to eliminate the outer exponent and then multiply the result, hopefully giving the same result:

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

`(2^color(red)(2) * 3^color(red)(2))^color(blue)(3) = 2^(color(red)(2) xx color(blue)(3)) * 3^(color(red)(2) xx color(blue)(3)) = 2^6 * 3^6 = 64 * 729 = 46,656`

yet another method is to rewrite the internal squares of the two numbers:

`(2^2 * 3^2)^3 = ((2 * 3)^2)^3 = (6^2)^3 = 36^3 = 46,656`