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(1/16)^-3/2

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

Simplifying (1/16)^(-3/2)

This problem involves simplifying a fractional exponent. Let's break down the steps:

Understanding Fractional Exponents

A fractional exponent like (-3/2) signifies both a root and a power. The denominator (2) indicates the root (in this case, square root), and the numerator (3) indicates the power.

Applying the Rules

  1. Negative Exponent: A negative exponent means we take the reciprocal of the base.

    Therefore, (1/16)^(-3/2) becomes (16)^(3/2)

  2. Fractional Exponent: Now we apply the root and power:

    • Square root: √16 = 4
    • Cube: 4^3 = 64

Final Answer

Therefore, (1/16)^(-3/2) simplifies to 64.

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