Which number is equivalent to \( \frac{3^4}{3^2} \)?

Answer

To simplify \( \frac{3^4}{3^2} \), we can use the properties of exponents. According to the quotient rule of exponents, if you have \( \frac{a^m}{a^n} \), it simplifies to \( a^{m-n} \). Therefore, we can apply this rule as follows: 1. Identify the base and the exponents: Here the base is 3, the numerator's exponent is 4 (\( m = 4 \)), and the denominator's exponent is 2 (\( n = 2 \)). 2. Subtract the exponents: \( m - n = 4 - 2 = 2 \). 3. Rewrite the expression: This gives us \( 3^{4-2} = 3^2 \). 4. Calculate \( 3^2 \): Now we calculate \( 3^2 = 3 \times 3 = 9 \). Thus, \( \frac{3^4}{3^2} = 3^2 = 9 \). The answer is B: 9.