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Multiply.
[tex]\[8v \cdot 3u^8 \cdot 2v^2 u^4\][/tex]

Simplify your answer as much as possible.

Sagot :

GinnyAnswer
To simplify the expression [tex]\( 8v \cdot 3u^8 \cdot 2v^2u^4 \)[/tex], follow these steps:

1. Multiply the numerical coefficients:
- The numerical coefficients in the expression are [tex]\( 8 \)[/tex], [tex]\( 3 \)[/tex], and [tex]\( 2 \)[/tex].
- To find the product of these coefficients, multiply them together:
[tex]\[ 8 \times 3 \times 2 = 48 \][/tex]

2. Combine the exponents of the variable [tex]\( u \)[/tex]:
- The expression has [tex]\( u \)[/tex] raised to different powers: [tex]\( u^8 \)[/tex] and [tex]\( u^4 \)[/tex].
- Use the laws of exponents, which state that when you multiply powers of the same base, you add the exponents:
[tex]\[ u^8 \cdot u^4 = u^{8 + 4} = u^{12} \][/tex]

3. Combine the exponents of the variable [tex]\( v \)[/tex]:
- The expression has [tex]\( v \)[/tex] raised to different powers: [tex]\( v \)[/tex] and [tex]\( v^2 \)[/tex].
- Recall that [tex]\( v \)[/tex] is equivalent to [tex]\( v^1 \)[/tex].
- Similar to the previous step, add the exponents:
[tex]\[ v^1 \cdot v^2 = v^{1 + 2} = v^3 \][/tex]

4. Combine all the parts together:
- Bring together the coefficient with the simplified powers of [tex]\( u \)[/tex] and [tex]\( v \)[/tex]:
[tex]\[ 48 \cdot u^{12} \cdot v^3 \][/tex]

Therefore, the simplified expression is:
[tex]\[ 48u^{12}v^3 \][/tex]
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