QuestionMultiply and simplify: $3 w^{9} \cdot 2 v^{7} w^{4} \cdot 8 v$ .

Studdy Solution

STEP 1

Assumptions1. We are multiplying three terms $3 w^{9}$ , $v^{7} w^{4}$ , and $8 v$ . . The multiplication is associative and commutative, which means we can multiply the terms in any order.
3. The laws of exponents apply, which means when multiplying terms with the same base, we add the exponents.

STEP 2

First, we can multiply the coefficients (the numbers) together. $Coefficient = \cdot2 \cdot8$

STEP 3

Calculate the coefficient.
$Coefficient =3 \cdot2 \cdot8 =48$

STEP 4

Next, we multiply the terms with the base $w$ . According to the laws of exponents, we add the exponents.
$w\, term = w^{9} \cdot w^{4}$

STEP 5

Calculate the $w$ term.
$w\, term = w^{9+4} = w^{13}$

STEP 6

Then, we multiply the terms with the base $v$ . $v\, term = v^{} \cdot v$

STEP 7

Calculate the $v$ term.
$v\, term = v^{7+1} = v^{}$

STEP 8

Finally, we combine the coefficient, the $w$ term, and the $v$ term to get the final answer.
$Answer = Coefficient \cdot w\, term \cdot v\, term$

STEP 9

Plug in the values for the coefficient, the $w$ term, and the $v$ term to get the final answer.
$Answer =48 \cdot w^{13} \cdot v^{8}$

STEP 10

The final answer is $48 w^{13} v^{8}$ .
The product of $3 w^{9}$ , $2 v^{7} w^{4}$ , and $8 v$ is $48 w^{13} v^{8}$ .

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