Math Problem Statement

Evaluate. Write your answer as a whole number or as a simplified fraction: 6^5 / 6^2

Solution

The expression to evaluate is:

6562\frac{6^5}{6^2}

Using the property of exponents aman=amn\frac{a^m}{a^n} = a^{m-n}, we can subtract the exponents:

652=636^{5-2} = 6^3

Now, calculate 636^3:

63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216

So, the simplified result is:

216\boxed{216}

Would you like more details or have any questions?

Here are some related questions:

  1. How would the result change if the base was different, say 55/525^5 / 5^2?
  2. What is the general rule for dividing exponents with the same base?
  3. How can we calculate higher powers of numbers efficiently?
  4. Can we extend the exponent rule to fractional or negative exponents?
  5. What is the value of 606^0 and why?

Tip: When dividing powers with the same base, just subtract the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Division of Powers

Formulas

a^m / a^n = a^(m-n)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8