%5E3-expanded.jpeg "(3x)^3 Expanded")
(3x)^3 Expanded: Understanding the Power of Exponents
In mathematics, exponents play a crucial role in simplifying complex expressions and equations. One such example is the expression (3x)^3, which can be expanded to reveal a fascinating pattern. In this article, we will delve into the world of exponents and explore the expansion of (3x)^3.
What is Exponentiation?
Exponentiation is a mathematical operation that involves raising a number or expression to a power. In the case of (3x)^3, the base is 3x, and the exponent is 3. The exponent indicates how many times the base should be multiplied by itself.
Expanding (3x)^3
To expand (3x)^3, we can use the property of exponentiation, which states that:
(a^m)^n = a^(mn)
In this case, a = 3x, m = 1, and n = 3. Applying the property, we get:
(3x)^3 = (3x)^(1*3) = (3x)^3
Now, let's expand the expression using the distributive property of multiplication:
(3x)^3 = 3^3 * x^3 = 27x^3
Breaking Down the Expansion
The expansion of (3x)^3 reveals an interesting pattern:
- The base
3is raised to the power of3, resulting in27. - The variable
xis also raised to the power of3, resulting inx^3. - The final result is the product of
27andx^3, which is27x^3.
Conclusion
In conclusion, expanding (3x)^3 helps us understand the power of exponents in simplifying complex expressions. By applying the properties of exponentiation and the distributive property of multiplication, we can break down the expression into its constituent parts and reveal a fascinating pattern. The result, 27x^3, is a testament to the elegance and beauty of mathematics.
