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(27/64)^-1/3

less than a minute read Jun 16, 2024
(27/64)^-1/3

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

This expression involves both fractions and exponents, so let's break it down step by step.

Understanding the Properties of Exponents

  • Negative exponents: A negative exponent means taking the reciprocal of the base. For example, x⁻¹ = 1/x.
  • Fractional exponents: A fractional exponent represents a root. For example, x^(1/n) is the nth root of x.

Applying the Properties

  1. Dealing with the negative exponent: (27/64)^(-1/3) = 1 / (27/64)^(1/3)

  2. Finding the cube root: 1 / (27/64)^(1/3) = 1 / (∛(27/64))

  3. Simplifying the cube root: 1 / (∛(27/64)) = 1 / (3/4)

  4. Dividing by a fraction: 1 / (3/4) = 1 * (4/3) = 4/3

Conclusion

Therefore, (27/64)^(-1/3) simplifies to 4/3.

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