3%E2%81%844.jpeg "(16/81)3⁄4")
(16/81)3⁄4: Understanding the Fractional Exponent
In mathematics, fractional exponents can be a bit confusing, but with a solid understanding of the rules and properties, they can become second nature. In this article, we'll delve into the world of fractional exponents by exploring the expression (16/81)3⁄4.
What is a Fractional Exponent?
A fractional exponent is a power that is a fraction. It's a way of expressing a root operation as a power. For example, a^(1/n) is equivalent to the n-th root of a. In our case, (16/81)3⁄4 is a fractional exponent expression.
Breaking Down the Expression
Let's break down the expression (16/81)3⁄4:
- The numerator is
16, and the denominator is81. - The fractional exponent is
3/4.
Evaluating the Expression
To evaluate (16/81)3⁄4, we need to follow the order of operations (PEMDAS):
- Raise
16to the power of3/4. - Raise
81to the power of3/4. - Divide the results.
Raising 16 to the Power of 3/4
16^(3/4) = (16^(1/4))^3
Since 16 = 2^4, we can rewrite the expression as:
(2^4)^(1/4) = 2
2^3 = 8
So, 16^(3/4) = 8.
Raising 81 to the Power of 3/4
81^(3/4) = (81^(1/4))^3
Since 81 = 3^4, we can rewrite the expression as:
(3^4)^(1/4) = 3
3^3 = 27
So, 81^(3/4) = 27.
Final Answer
Now, let's divide the results:
(16/81)^(3/4) = 8/27
And that's the final answer!
Conclusion
In this article, we explored the expression (16/81)3⁄4 and evaluated it by following the order of operations. We broke down the expression, raised the numerator and denominator to the power of 3/4, and finally divided the results to get the final answer.
