Final answer:
To simplify the given expression, we multiply the coefficients and combine the variables with like bases by adding their exponents, resulting in a final simplified expression of 84/(y^2*v^3) using only positive exponents.
Step-by-step explanation:
To simplify the expression 7y^(-6)v^(-4)*2vy^(4)*6u^(-9)u^(9) using only positive exponents, we will apply the rules of exponents for multiplication and division:
- Multiply coefficients together: 7*2*6 = 84.
- Combine like terms by adding or subtracting exponents, remembering that u^(-9)u^(9) = u^0 = 1, since anything raised to the power of zero equals one.
- As a result, the u terms cancel each other out, and we only need to combine the y and v terms.
- y^(-6+y^4) = y^(4-6) = y^(-2) and since we need positive exponents, we write this as 1/y^2.
- Similarly, v^(-4)v^1 = v^(1-4) = v^(-3), which is written as 1/v^3 with a positive exponent.
- Combine all simplified terms to get the final answer: 84/(y^2*v^3).
The answer demonstrates proper use of exponents and simplification of algebraic expressions.
Always check to see if the answer is reasonable and all terms with negative exponents have been converted to their positive counterparts.