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(1/9)^-3/2

less than a minute read Jun 16, 2024
(1/9)^-3/2

Simplifying (1/9)^(-3/2)

This problem involves working with fractional exponents, which can be a bit intimidating at first, but it's actually quite straightforward. Let's break down the steps:

Understanding Fractional Exponents

A fractional exponent like (-3/2) represents both a root and a power. The denominator (2) indicates a square root, and the numerator (-3) indicates a power of -3.

Applying the Rules

  1. Negative exponent: The negative exponent indicates we need to take the reciprocal of the base.

    (1/9)^(-3/2) = (9/1)^(3/2)

  2. Fractional exponent: We can now separate the square root and the power of 3:

    (9/1)^(3/2) = (√(9/1))^3

  3. Simplify:

    (√(9/1))^3 = (3)^3 = 27

Conclusion

Therefore, (1/9)^(-3/2) simplifies to 27.

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