Question

Multiply. 3u*2u⁵ w² *3w⁹ Simplify your answer as much as possible.

Answer 1

The final answer is 6u³w¹¹, obtained by multiplying the coefficients and combining like terms. This simplified expression represents the result of multiplying 3u*2u⁵w² by 3w⁹.

Step-by-step explanation:

The given expression is
`\(3u \cdot 2u^5 \cdot w^2 \cdot 3w^9\)`. To simplify this expression, we can multiply the coefficients (3 and 2) together, as well as the variables with the same base (u and w).

First, multiplying the coefficients:
`\(3 * 2 = 6\)`.

Now, for the variables:

- For 'u': \
`(u^1 * u^5 = u^(1+5) = u^6\))`

- For 'w':
`\(w^2 * w^9 = w^(2+9) = w^(11)\)`

Putting it all together, the simplified expression is
`\(6u^6w^(11)\)`.

So, the final answer is
`\(6u^3w^(11)\)`.

In summary, when multiplying the terms, we combined the coefficients and applied the rules of exponents to simplify the variables. This resulted in the expression
`\(6u^3w^(11)\)`, where 6 is the product of the coefficients,
`\(u^3\)` is the simplified term for 'u', and
`\(w^(11)\)` is the simplified term for 'w'.