(64/27)^-1/3

2 min read Jun 16, 2024

Simplifying (64/27)^(-1/3)

This expression involves both fractional exponents and negative exponents. Let's break it down step by step:

Understanding Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. In other words:

x^-n = 1/x^n

Understanding Fractional Exponents

A fractional exponent represents a root. The denominator of the fraction indicates the type of root. For example:

x^(1/n) = nth root of x

Applying the Rules

Reciprocal: First, we address the negative exponent. (64/27)^(-1/3) becomes (27/64)^(1/3).
Cube Root: Now we deal with the fractional exponent. (27/64)^(1/3) is the cube root of (27/64).
Calculation: The cube root of 27 is 3, and the cube root of 64 is 4. Therefore, the simplified answer is 3/4.

In Conclusion

(64/27)^(-1/3) simplifies to 3/4. By applying the rules of exponents, we were able to break down the expression and arrive at a simple numerical answer.