(27^5/3)^1/5

Jasonbradley

2 min read

·

Jun 16, 2024

12

Share

Simplifying the Expression (27^(5/3))^(1/5)

This article explores the simplification of the expression (27^(5/3))^(1/5). We will use the properties of exponents to break down the expression and arrive at a simplified answer.

Understanding Exponent Properties

To simplify the expression, we need to understand these key properties of exponents:

• Power of a power: (x^m)^n = x^(m*n)
• Fractional exponent: x^(m/n) = (x^m)^(1/n) = (x^(1/n))^m

Simplifying the Expression

1. Applying the power of a power property: We can simplify the expression by multiplying the exponents inside the parentheses:

   (27^(5/3))^(1/5) = 27^((5/3)*(1/5)) = 27^(1/3)

2. Applying the fractional exponent property: We can rewrite the expression as a cube root:

   27^(1/3) = ³√27

3. Evaluating the cube root: The cube root of 27 is 3:

   ³√27 = 3

Conclusion

Therefore, the simplified form of (27^(5/3))^(1/5) is 3.