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Simplifying Exponents: (x^3)^3 = x^n
In mathematics, understanding exponent rules is crucial for simplifying expressions and solving equations. One common rule involves raising a power to another power, like in the expression (x^3)^3 = x^n. Let's break down how to determine the value of 'n'.
Understanding the Rule
The rule for simplifying expressions of this form is: (x^m)^n = x^(m*n). This means that when raising a power to another power, we multiply the exponents together.
Applying the Rule
In our example, (x^3)^3, we have m = 3 and n = 3. Applying the rule, we get:
(x^3)^3 = x^(3*3) = x^9
Therefore, n = 9.
Example
Let's consider another example: (y^2)^5 = y^n.
- Applying the rule: (y^2)^5 = y^(2*5) = y^10
- Therefore, n = 10.
Importance
Understanding this rule is essential for various mathematical operations, including:
- Simplifying algebraic expressions
- Solving exponential equations
- Working with scientific notation
By consistently applying the rule, you can efficiently simplify complex expressions involving exponents and solve a wider range of mathematical problems.