(4a)^3/a^5

Jasonbradley

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Jun 16, 2024

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Simplifying (4a)^3 / a^5

This article will guide you through the process of simplifying the algebraic expression (4a)^3 / a^5.

Understanding the Expression

• (4a)^3: This represents the cube of the entire term (4a), meaning it is multiplied by itself three times: (4a) * (4a) * (4a).
• a^5: This represents 'a' multiplied by itself five times: a * a * a * a * a.
• Division: The entire expression is a division problem where (4a)^3 is the numerator and a^5 is the denominator.

Simplifying the Expression

1. Simplify the numerator:

   • (4a)^3 = (4a) * (4a) * (4a) = 64a^3

2. Rewrite the expression:

   • The expression now becomes 64a^3 / a^5

3. Apply the rule of exponents for division:

   • When dividing exponents with the same base, subtract the powers.
   • 64a^(3-5) = 64a^(-2)

4. Convert negative exponents to positive exponents:

   • a^(-2) = 1/a^2

5. Combine the terms:

   • 64a^(-2) = 64 * (1/a^2) = 64/a^2

Final Result

The simplified form of the expression (4a)^3 / a^5 is 64/a^2.