3.jpeg "(-4ab)3")
Simplifying (-4ab)³
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves dealing with exponents and parentheses. Let's explore how to simplify the expression (-4ab)³.
Understanding the Exponent
The exponent "3" indicates that we are multiplying the base, which is (-4ab), by itself three times:
(-4ab)³ = (-4ab) * (-4ab) * (-4ab)
Applying the Power of a Product Rule
A helpful rule to remember is the power of a product rule: (ab)ⁿ = aⁿbⁿ. This rule states that when a product is raised to a power, each factor within the product is raised to that power.
Applying this rule to our expression:
(-4ab)³ = (-4)³ * a³ * b³
Calculating the Result
Now we can calculate each term separately:
- (-4)³ = -64 (Since a negative number raised to an odd power remains negative)
- a³ = a * a * a
- b³ = b * b * b
Combining the terms:
(-4ab)³ = -64a³b³
Conclusion
Therefore, the simplified form of (-4ab)³ is -64a³b³. Remember to apply the appropriate rules of exponents when simplifying expressions, and pay attention to the signs of the terms.