%5E3-expanded-form.jpeg "(3x)^3 Expanded Form")
Expanded Form of (3x)^3
In algebra, when we raise an expression to a power, we can use the rule of exponents to simplify the expression. In this case, we want to find the expanded form of (3x)^3.
What is the Expanded Form?
The expanded form of an expression is the simplified form of the expression without any exponents or parentheses. To find the expanded form of (3x)^3, we need to follow the rule of exponents, which states that:
(a^m)^n = a^(m*n)
In our case, a = 3x, m = 1, and n = 3.
Expanding the Expression
Using the rule of exponents, we can expand the expression as follows:
(3x)^3 = (3x)^(1*3) = (3x)^3
To simplify this expression, we need to multiply the 3x by itself three times:
(3x)^3 = 3x * 3x * 3x
Now, we can multiply the coefficients (the numbers) and the variables (the x's) separately:
3x * 3x * 3x = (3*3*3) * (x*x*x)
3x * 3x * 3x = 27x^3
So, the expanded form of (3x)^3 is 27x^3.
Conclusion
In conclusion, the expanded form of (3x)^3 is 27x^3. This is obtained by applying the rule of exponents and simplifying the expression by multiplying the coefficients and variables separately.
