Answer :
Final answer:
The given expression (-6x^(6)v^(2) + 13x^(6)v^(6)) / (-2x^(2)v^(3)) simplifies to 3x^4/v. This is achieved by dividing the coefficients and subtracting the exponents of similar bases, followed by rearranging any terms with negative exponents.
Explanation:
To solve the provided expression, we need to use the laws of exponents and properties of division. Since we are dividing two expressions with similar bases, we subtract the exponents. Let's break down the expression piece by piece.
- For -6x^(6)v^(2) / -2x^(2)v^(3), we can simplify the coefficients -6/ -2 to get 3. Now we have 3x^(6)v^(2) / x^(2)v^(3).
- Using the properties of exponents, we subtract the exponents of similar bases. x^(6) / x^(2) becomes x^(6-2) = x^(4), and v^(2) / v^(3) becomes v^(2-3) = v^(-1).
- Finally, the simplified version of the expression is 3x^(4)v^(-1).
Remember, a negative exponent means that the base is on the wrong side of the fraction line, so you can flip the base to the other side (i.e, the reciprocal) to make the exponent positive.
Hence, the further simplified expression would be 3x^(4) / v.
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