Math Problem Statement

Rewrite as a base to a​ power, if possible. 6^4x6^5

Solution

To rewrite the expression 64×656^4 \times 6^5 as a base to a power, you can use the product of powers property. This property states that:

am×an=am+na^m \times a^n = a^{m+n}

Here, the base aa is 66, and the exponents are 44 and 55. Applying the rule:

64×65=64+5=696^4 \times 6^5 = 6^{4+5} = 6^9

Thus, 64×65=696^4 \times 6^5 = 6^9.

Would you like more details on exponent rules, or do you have any other questions?

Here are 5 related questions:

  1. How would you simplify 23×272^3 \times 2^7?
  2. What is (32)3(3^2)^3 using the power of a power rule?
  3. How do you simplify 56/525^6 / 5^2?
  4. Can you rewrite 70×757^0 \times 7^5 as a single exponent?
  5. What is the result of 104×10010^4 \times 10^0?

Tip: When multiplying numbers with the same base, always add the exponents!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Properties of Exponents

Formulas

a^m * a^n = a^(m+n)

Theorems

Product of Powers Property

Suitable Grade Level

Grades 6-8