(3^-8x7^3)^-2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (3^-8 x 7^3)^-2

This article will walk you through the process of simplifying the expression (3^-8 x 7^3)^-2. We will utilize the rules of exponents to achieve this.

Understanding the Rules of Exponents

Before we dive into the simplification, let's review the relevant rules of exponents:

• Product of powers: x^m * x^n = x^(m+n)
• Power of a power: (x^m)^n = x^(m*n)
• Negative exponent: x^-n = 1/x^n

Simplifying the Expression

1. Apply the power of a power rule: (3^-8 x 7^3)^-2 = 3^(-8*-2) * 7^(3*-2)

2. Simplify the exponents: 3^(16) * 7^(-6)

3. Apply the negative exponent rule: 3^(16) * 1/7^6

4. Rewrite the expression: 3^(16) / 7^6

Final Result

The simplified form of the expression (3^-8 x 7^3)^-2 is 3^(16) / 7^6. While you could calculate the actual values of 3^16 and 7^6, this simplified form is often preferred as it is easier to work with in further calculations.