Simplify $3^2 \times 3^3$.
A) 3
B) $3^8$
C) $3^6$
D) $3^5$
Answer (1)
Use the property of exponents: a m × a n = a m + n .
Apply this property to the given expression: 3 2 × 3 3 = 3 2 + 3 .
Simplify the exponent: 2 + 3 = 5 .
The simplified expression is 3 5 .
Explanation
Understanding the problem We are asked to simplify the expression 3 2 × 3 3 . We need to use the properties of exponents to simplify this expression.
Using the exponent property The property of exponents that we will use is: a m × a n = a m + n , where a is the base and m and n are the exponents.
Applying the property Applying this property to the given expression, we have: 3 2 × 3 3 = 3 2 + 3 .
Simplifying the exponent Now, we simplify the exponent: 2 + 3 = 5 . Therefore, 3 2 × 3 3 = 3 5 .
Finding the answer The simplified expression is 3 5 . Comparing this with the given options, we see that option D matches our simplified expression. Therefore, the correct answer is D.
Examples
Exponents are used to calculate compound interest. For example, if you invest 100 a t anann u a l in t eres t r a t eo f 5 n$ years is 100 × ( 1.05 ) n . Understanding exponents helps you calculate how your investment grows over time. This is a practical application of exponents in finance.
