(a/2)^4 (8a^5)^2/a^-1a^10

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (a/2)^4 (8a^5)^2/a^-1a^10

This article will guide you through simplifying the expression (a/2)^4 (8a^5)^2/a^-1a^10.

Understanding the Rules of Exponents

To simplify this expression, we'll need to apply several exponent rules:

• Power of a product: (ab)^n = a^n * b^n
• Power of a quotient: (a/b)^n = a^n/b^n
• Product of powers: a^m * a^n = a^(m+n)
• Quotient of powers: a^m / a^n = a^(m-n)
• Negative exponent: a^-n = 1/a^n

Step-by-Step Simplification

Let's break down the simplification step by step:

1. Apply the power of a quotient rule to (a/2)^4: (a/2)^4 = a^4 / 2^4

2. Apply the power of a product rule to (8a^5)^2: (8a^5)^2 = 8^2 * a^10

3. Combine the terms and simplify: (a^4/2^4) * (8^2 * a^10) / (a^-1 * a^10)

4. Apply the product of powers rule for the 'a' terms in the numerator and denominator: (a^(4+10)) * (8^2) / (2^4 * a^(-1+10))

5. Simplify further: a^14 * 64 / 16 * a^9

6. Apply the quotient of powers rule: a^(14-9) * 64/16

7. Simplify to get the final result: a^5 * 4

Final Result

Therefore, the simplified form of the expression (a/2)^4 (8a^5)^2/a^-1a^10 is 4a^5.