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Simplifying Expressions with Fractional Exponents: (x^4/3)(x^2/3)
In mathematics, especially when dealing with exponents, we often encounter expressions involving fractions. These expressions can seem daunting at first, but they follow the same rules of exponents as whole number exponents. This article will guide you through simplifying the expression (x^4/3)(x^2/3).
Understanding the Rules of Exponents
To simplify the expression, we need to recall the fundamental rules of exponents:
- Product of Powers: When multiplying exponents with the same base, we add the powers: x^m * x^n = x^(m+n)
- Power of a Power: When raising a power to another power, we multiply the exponents: (x^m)^n = x^(m*n)
Simplifying the Expression
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Identify the Base and Exponents: In our expression, x is the base, and 4/3 and 2/3 are the exponents.
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Apply the Product of Powers Rule: Since we are multiplying two terms with the same base, we add the exponents: (x^4/3)(x^2/3) = x^(4/3 + 2/3)
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Simplify the Exponent: Add the fractions in the exponent: x^(4/3 + 2/3) = x^(6/3)
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Simplify further: Reduce the fraction in the exponent: x^(6/3) = x^2
Final Result
Therefore, the simplified expression of (x^4/3)(x^2/3) is x^2.
This process demonstrates how even complex expressions with fractional exponents can be simplified using the fundamental rules of exponents. Remember, practice and familiarity with these rules are key to confidently handling such expressions.