(2x)^-4/x^-1*x

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2x)^-4/x^-1*x

This article will guide you through simplifying the expression (2x)^-4/x^-1*x. We'll break down the steps using the rules of exponents.

Understanding the Rules of Exponents

Before we begin, let's review some key exponent rules:

• Product of Powers: x^m * x^n = x^(m+n)
• Quotient 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. Simplify the numerator:

   • (2x)^-4 = 1/(2x)^4 (using the negative exponent rule)
   • 1/(2x)^4 = 1/(2^4 * x^4) = 1/(16x^4) (using the power of a power rule)

2. Simplify the denominator:

   • x^-1 = 1/x (using the negative exponent rule)

3. Rewrite the expression:

   • The original expression becomes: (1/(16x^4)) / (1/x) * x

4. Dividing by a fraction is the same as multiplying by its inverse:

   • (1/(16x^4)) * (x/1) * x

5. Simplify:

   • (x * x) / (16x^4) = x^2 / 16x^4

6. Apply the Quotient of Powers Rule:

   • x^2 / 16x^4 = 1 / (16x^(4-2)) = 1 / (16x^2)

Final Result

Therefore, the simplified form of the expression (2x)^-4/x^-1*x is 1 / (16x^2).