Question

How do you multiply `2w ^ { 9} u ^ { 7} \cdot 3w \cdot 2u ^ { 7}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(2 * 3 * 2)(w^9 * w)(u^7 * u^7) =>`

`12(w^9 * w)(u^7 * u^7)`

Now, use these rules of exponents to complete the multiplication of the `w` and `u` terms:

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

`12(w^9 * w)(u^7 * u^7) =>`

`12(w^color(red)(9) * w^color(blue)(1))(u^color(red)(7) * u^color(blue)(7)) =>`

`12w^(color(red)(9)+color(blue)(1))u^(color(red)(7)+color(blue)(7)) =>`

`12w^10u^14`

Answer 2

`12u^14w^10`

Explanation:

Just imagine yourself multiplying `3w` with `2w^9u^7` and `2u^7` with `2w^9u^7`, then multiplying these together

First let's do the w.

`2w^9*3w^1` (since `3w=3w^1`)

To multiply powers, you apply the following rule

`a^x*a^y=a^(x+y)`

`therefore 2w^9*3w^1=(2*3)w^(9+1)`
`=6w^10`

Same applies to the u.

`u^7*2u^7=2u^(7+7)`
`=2u^14`

Now obviously, `6*2=12`

Combining them, we get `12u^14w^10` (`u` first because it has to be in alphabetical order)

Answer 3

`6u^14w^10`

Explanation:

The indices or exponents of a number of variable indicates how many of them are multiplied together.

`x^4 = x*x*x*x" "larr` remember `*` means `xx`

When we multiply in algebra we multiply all the same types of bases together.

`2*w^9u^7*3w*2u^7` can be re-arranged and written as:

`=color(blue)(2*3)*color(purple)(u^7*u^7)*color(forestgreen)(w^9*w^1)`

`=color(blue)(6)*color(purple)(u^14)*color(forestgreen)(w^10)`

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Recall:

Note that:

`color(purple)(u^7*u^7 =u*u*u*u*u*u*u xx u*u*u*u*u*u*u)`

`color(purple)(u^7*u^7 = u^14)" "larr` add the indices of like bases

`color(forestgreen)(w^9*w^1 = w*w*w*w*w*w*w*w*wxxw = w^10`

`color(blue)(2*3=6" "larr" "2 and 3` are just numbers, multiply as usual.