Rewrite the product as an exponent: $3^3 \cdot 3^3$
Answer (1)
We are given the expression 3 3 ⋅ 3 3 .
Apply the exponent property a m ⋅ a n = a m + n to get 3 3 + 3 .
Simplify the exponent to get 3 6 .
The product 3 3 ⋅ 3 3 rewritten as an exponent is 3 6 .
Explanation
Understanding the problem We are given the expression 3 3 ⋅ 3 3 . Our goal is to rewrite this product as a single exponent. To do this, we will use the property of exponents that states when you multiply two exponents with the same base, you add the exponents.
Applying the exponent property The property of exponents we will use is: a m ⋅ a n = a m + n In our case, the base is 3, and the exponents are both 3. So, we have: 3 3 ⋅ 3 3 = 3 3 + 3
Simplifying the exponent Now, we simply add the exponents: 3 + 3 = 6 So, our expression becomes: 3 6
Final Answer Therefore, the product 3 3 ⋅ 3 3 can be rewritten as 3 6 .
Examples
Exponents are used to calculate areas and volumes. For example, if you want to find the volume of a cube with side length 3, you would calculate 3 3 = 3 ⋅ 3 ⋅ 3 = 27 . When you have multiple cubes with the same side length and want to find the total volume, you can use the properties of exponents to simplify the calculation. For instance, if you have two such cubes, the total volume would be 3 3 ⋅ 2 = 27 ⋅ 2 = 54 . If you have two cubes and want to find the volume of a bigger cube that has sides twice as long, you calculate ( 2 ⋅ 3 ) 3 = 6 3 = 216 .
