If 2^12 * 2^12 = 2^n, what is the value of n?
Understand the Problem
The question is asking to find the value of 'n' in the equation 2^12 × 2^12 = 2^n. This involves using the properties of exponents to simplify the left side of the equation and then equating the exponents to solve for 'n'.
Answer
$n=24$
Answer for screen readers
$n = 24$
Steps to Solve
- Apply the product of powers rule
When multiplying exponential expressions with the same base, you add the exponents
$2^{12} \times 2^{12} = 2^{12+12}$
- Simplify the exponent
Add the exponents on the right side of the equation
$2^{12+12} = 2^{24}$
- Equate the exponents
Since the bases are equal, the exponents must be equal
$2^{24} = 2^{n}$ therefore $n = 24$
$n = 24$
More Information
The problem demonstrates a fundamental property of exponents where multiplying powers with the same base results in adding their exponents. This rule is widely used in simplifying expressions and solving equations involving exponents.
Tips
A common mistake is to multiply the exponents instead of adding them when multiplying numbers with the same base. Remember the rule: $a^m \times a^n = a^{m+n}$, not $a^{m \times n}$.
AI-generated content may contain errors. Please verify critical information
