Question

Multiply and find the excluded values.
4/3 a² .b .c . (6bc/8w)

Answer 1

The excluded values of the given exxpression 4/3 a² .b .c . (6bc/8w) is

`\[ (2)/(w) a^2 b^2 c^2 \]`

Step-by-step explanation:

The given expression is
`\((4)/(3)a^2bc \cdot (6bc)/(8w)\)`. To simplify this expression, we can multiply the numerators and denominators separately.

The numerator becomes
`\(4 \cdot 6 = 24\),` and the denominator becomes
`\(3 \cdot 8 = 24w\)`. Thus, the expression becomes
`\((24)/(24w)\)`, which simplifies to
`\((1)/(w)\)`.

Now, the simplified expression is
`\((1)/(w) \cdot a^2bc\).` To further simplify this expression, we can rearrange the terms, resulting in
`\((a^2b^2c^2)/(w)\)`.

Therefore, the final answer to the given expression is
`\((2)/(w) a^2 b^2 c^2\).`

In summary, by multiplying the terms in the given expression and simplifying, we obtain the final result
`\((2)/(w) a^2 b^2 c^2\)`. The calculation involves straightforward multiplication and cancellation of common factors. This process ensures a clear and concise solution to the given mathematical expression.

Answer 2

To multiply the expression 4/3 a².b.c. (6bc/8w), simplify the numbers as (4/3) * (6/8) and multiply the variables as a² * b * c * bc. After simplifying, the final expression is a² * b² * c² / w, with the excluded value being w ≠ 0 to prevent division by zero.

Step-by-step explanation:

To multiply and find the excluded values for the expression 4/3 a² .b .c . (6bc/8w), you must first simplify the expression and then determine the values for which the variable in the denominator cannot be set equal to zero, as they would make the expression undefined.

Let's multiply the fractions:

Simplify the numbers: (4/3) * (6/8) = 4/3 * 3/4 = 1 (since 6/8 reduces to 3/4).

Multiply the variables: a² * b * c * bc = a² * b² * c².

Combine the two parts: 1 * a² * b² * c² / w.

The final simplified expression is a² * b² * c² / w.

In terms of excluded values, w cannot be zero because division by zero is undefined.

Therefore, the simplified expression is a² * b² * c² / w, where w ≠ 0.