(49/4)1/2 X (81/16)-1/4

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (49/4)^1/2 x (81/16)^-1/4

This article will guide you through simplifying the given expression: (49/4)^1/2 x (81/16)^-1/4. We'll break down the steps and explain the reasoning behind each.

Understanding the Concepts

• Fractional Exponents: A fractional exponent like 1/2 represents a square root, and 1/4 represents a fourth root.
• Negative Exponents: A negative exponent indicates a reciprocal. For example, (a/b)^-n = (b/a)^n

Step-by-Step Simplification

1. Simplify the Square Root:

   • (49/4)^1/2 = √(49/4) = 7/2

2. Simplify the Fourth Root:

   • (81/16)^-1/4 = (16/81)^1/4 = √⁴(16/81) = 2/3

3. Multiply the Simplified Terms:

   • (7/2) x (2/3) = 14/6 = 7/3

Final Answer

Therefore, the simplified expression of (49/4)^1/2 x (81/16)^-1/4 is 7/3.