How do you multiply #(8w^2)/9*3/(2w^4)#?

Question

Genesis Allen · Accepted Answer

See a solution process below:

First, we can rewrite the expression as: #((8 * 3)/(9 * 2))(w^2/w^4) => ((color(red)(cancel(color(black)(8)))4 * color(blue)(cancel(color(black)(3))))/(color(blue)(cancel(color(black)(9)))3 * color(red)(cancel(color(black)(2)))))(w^2/w^4) =># #4/3(w^2/w^4)# We can now use this rule for exponents to simplify the #w# terms: #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))# #4/4(w^color(red)(2)/w^color(blue)(4)) => 4/3 * 1/w^(color(blue)(4)-color(red)(2)) => 4/3 * 1/w^2 =># #4/(3w^2)#

Ethan Adkins · Answer

undefined To multiply (8w^2)/9 * 3/(2w^4), you can simplify the expression by multiplying the numerators and denominators separately.

First, multiply the numerators: 8w^2 * 3 = 24w^2.

Next, multiply the denominators: 9 * 2w^4 = 18w^4.

Finally, write the result as a fraction: (24w^2)/(18w^4).

To simplify the fraction, divide both the numerator and denominator by the greatest common factor, which is 6w^2.

Dividing the numerator by 6w^2: 24w^2 ÷ 6w^2 = 4.

Dividing the denominator by 6w^2: 18w^4 ÷ 6w^2 = 3w^2.

Therefore, the simplified expression is 4/3w^2.