%5E3%2F-6v%5E-2.jpeg "(2v^4)^3/-6v^-2")
Simplifying the Expression (2v^4)^3/-6v^-2
This article will guide you through simplifying the expression (2v^4)^3/-6v^-2. We'll break down the steps using the rules of exponents and provide a clear explanation.
Step 1: Simplifying the Numerator
We start by simplifying the numerator (2v^4)^3. To do this, we apply the power of a product rule and the power of a power rule:
(ab)^n = a^n * b^n (a^m)^n = a^(m*n)
Applying these rules to our expression:
(2v^4)^3 = 2^3 * (v^4)^3 = 8 * v^(4*3) = 8v^12
Step 2: Simplifying the Denominator
Now, let's simplify the denominator -6v^-2. This involves using the rule for negative exponents:
a^-n = 1/a^n
Applying this rule:
-6v^-2 = -6 * (1/v^2) = -6/v^2
Step 3: Combining the Simplified Terms
We now have the simplified numerator and denominator:
8v^12 / (-6/v^2)
To simplify further, we can multiply the numerator by the reciprocal of the denominator:
8v^12 * (v^2 / -6)
Finally, simplifying the expression:
-4/3 * v^(12+2) = -4/3 * v^14
Conclusion
Therefore, the simplified form of the expression (2v^4)^3/-6v^-2 is -4/3 * v^14.