If 2^12 * 2^12 = 2^n what is the value of n?
Understand the Problem
The question involves simplifying an expression with exponents and solving for an unknown variable 'n'. We need to use the rules of exponents to simplify the left side of the equation and then determine the value of 'n'.
Answer
$n = 4$
Answer for screen readers
$n = 4$
Steps to Solve
- Simplify the left side using exponent rules
We are given the equation:
$9^6 \times 9^{-2} = 9^n$
Using the rule $a^m \times a^n = a^{m+n}$, we can simplify the left side:
$9^{6 + (-2)} = 9^n$
- Simplify the exponent
Adding the exponents:
$9^{6 - 2} = 9^n$
$9^4 = 9^n$
- Solve for n
Since the bases are the same, we can equate the exponents:
$4 = n$
Therefore, $n = 4$.
$n = 4$
More Information
The problem uses the fundamental property of exponents where multiplying powers with the same base results in adding the exponents. This is a core concept in algebra.
Tips
A common mistake is incorrectly applying the exponent rules, such as multiplying the exponents instead of adding them when the bases are multiplied. Another mistake is not handling negative exponents correctly.
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