Simplify the expression below.
$3^4 \times 3^2$
A. $3^4$
B. $3^6$
C. $3^8$
D. $9^8$
Answer (1)
The problem requires simplifying the expression 3 4 × 3 2 using exponent rules.
Apply the rule a m × a n = a m + n .
Add the exponents: 4 + 2 = 6 .
The simplified expression is 3 6 .
The final answer is 3 6 .
Explanation
Understanding the Problem We are given the expression 3 4 × 3 2 and asked to simplify it. We need to use the properties of exponents to combine these terms.
Applying the Exponent Rule The key property we'll use is that when multiplying exponential terms with the same base, we add the exponents: a m × a n = a m + n .
Combining the Exponents Applying this rule to our expression, we have 3 4 × 3 2 = 3 4 + 2 .
Calculating the New Exponent Now, we simply add the exponents: 4 + 2 = 6 . Therefore, 3 4 × 3 2 = 3 6 .
Selecting the Correct Option Comparing our simplified expression 3 6 to the given options, we see that it matches option B.
Final Answer Therefore, the simplified expression is 3 6 .
Examples
Understanding exponent rules is crucial in many areas, such as calculating compound interest. For example, if you invest money that grows at a rate of 5% annually, the value of your investment after 10 years can be calculated using exponents. Similarly, in computer science, exponents are used to measure the complexity of algorithms. Simplifying expressions with exponents helps in making these calculations easier and more efficient.
