%5E7.jpeg "(x^7/y^9)^7")
Simplifying Expressions with Exponents
In mathematics, simplifying expressions is a fundamental skill. One common type of simplification involves expressions with exponents. Today we'll explore how to simplify the expression (x^7/y^9)^7.
Understanding the Rules
To simplify this expression, we need to recall a few key rules regarding exponents:
- The power of a quotient rule: (a/b)^n = a^n/b^n. This rule states that when raising a fraction to a power, we raise both the numerator and denominator to that power.
- The power of a power rule: (a^m)^n = a^(m*n). This rule states that when raising a power to another power, we multiply the exponents.
Simplifying the Expression
Let's apply these rules to our expression:
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Apply the power of a quotient rule: (x^7/y^9)^7 = x^(77) / y^(97)
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Apply the power of a power rule: x^(77) / y^(97) = x^49 / y^63
Result
Therefore, the simplified form of (x^7/y^9)^7 is x^49 / y^63.
Key Takeaways
Simplifying expressions with exponents requires a thorough understanding of the relevant rules. By applying these rules correctly, we can efficiently reduce complex expressions to their simplest forms.