%5E3.jpeg "(6x^4y)^3")
Simplifying (6x^4y)^3
This article will explore the process of simplifying the expression (6x^4y)^3.
Understanding the Exponent
The expression (6x^4y)^3 indicates that the entire term within the parentheses, (6x^4y), is being multiplied by itself three times.
Applying the Power of a Product Rule
To simplify this, we can apply the power of a product rule: (ab)^n = a^n * b^n. This rule states that when raising a product to a power, we can raise each factor to that power individually.
Simplifying the Expression
Let's apply the rule to our expression:
(6x^4y)^3 = 6^3 * (x^4)^3 * y^3
Now, we can simplify each term:
- 6^3 = 6 * 6 * 6 = 216
- (x^4)^3 = x^(4*3) = x^12
- y^3 = y^3
Combining these results, we obtain the simplified expression:
(6x^4y)^3 = 216x^12y^3
Therefore, the simplified form of (6x^4y)^3 is 216x^12y^3.