Math Problem Statement

Which expression is equivalent to 12^(-7) * 12^2?

Solution

The problem asks which expression is equivalent to 127×12212^{-7} \times 12^2.

To solve this, we use the properties of exponents, specifically:

am×an=am+na^m \times a^n = a^{m+n}

Here, m=7m = -7 and n=2n = 2, so:

127×122=127+2=12512^{-7} \times 12^2 = 12^{-7 + 2} = 12^{-5}

Thus, the equivalent expression is 12512^{-5}. This matches the option "1/12^5", since 12512^{-5} can also be written as:

125=112512^{-5} = \frac{1}{12^5}

Would you like further details, or do you have any questions?

Related Questions:

  1. What is the rule for multiplying powers with the same base?
  2. How would you simplify a3×a4a^{-3} \times a^4?
  3. What is the significance of negative exponents in expressions?
  4. How do you handle division with exponents, such as a5a3\frac{a^5}{a^3}?
  5. What happens when you raise a power to another power, like (a3)2(a^3)^2?

Tip: When multiplying terms with the same base, remember to add the exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Powers

Formulas

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

Theorems

Exponent Multiplication Rule

Suitable Grade Level

Grades 7-9