%5E4.jpeg "(a^2/b^3)^4")
Simplifying (a^2/b^3)^4
This expression involves both exponents and fractions. Let's break down how to simplify it using the rules of exponents.
Understanding the Rules of Exponents
- Product of Powers: When multiplying powers with the same base, you add the exponents: x^m * x^n = x^(m+n)
- Power of a Power: When raising a power to another power, you multiply the exponents: (x^m)^n = x^(m*n)
- Power of a Quotient: When raising a quotient to a power, you raise both the numerator and the denominator to that power: (x/y)^n = x^n / y^n
Applying the Rules to Simplify
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Power of a Quotient: Apply the rule (x/y)^n = x^n / y^n to our expression: (a^2/b^3)^4 = a^(24) / b^(34)
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Power of a Power: Simplify the exponents: a^(24) / b^(34) = a^8 / b^12
Final Answer
Therefore, the simplified form of (a^2/b^3)^4 is a^8 / b^12.