To simplify the expression 3^5⋅3^7 using the Product Rule of Exponents, we need to add the exponents together while keeping the base the same.
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, we can add the exponents.
In our expression, we have 3^5⋅3^7. The base is 3, and we can add the exponents 5 and 7.
So 3^5⋅3^7 simplifies to 3^(5+7).
Adding the exponents gives us 3^12.
Therefore, 3^5⋅3^7 simplifies to 3^12.
Use the Product Rule of Exponents to simplify 3^5⋅3^7
Please explain the steps
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Can you please show the work
Certainly! Here's the step-by-step work:
We start with the expression 3^5⋅3^7.
According to the Product Rule of Exponents, we can add the exponents when multiplying two exponential expressions with the same base.
So, we add the exponents 5 and 7:
3^5⋅3^7 = 3^(5 + 7).
Adding the exponents gives us:
3^(5 + 7) = 3^12.
Therefore, 3^5⋅3^7 simplifies to 3^12.
We start with the expression 3^5⋅3^7.
According to the Product Rule of Exponents, we can add the exponents when multiplying two exponential expressions with the same base.
So, we add the exponents 5 and 7:
3^5⋅3^7 = 3^(5 + 7).
Adding the exponents gives us:
3^(5 + 7) = 3^12.
Therefore, 3^5⋅3^7 simplifies to 3^12.
According to the Product Rule of Exponents, we can add the exponents when multiplying two exponential expressions with the same base.
can you show
can you show
Sure! Here's a more detailed explanation of the steps involved:
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, we can add the exponents.
Given the expression 3^5⋅3^7, we have the base 3 and two exponents, 5 and 7.
To simplify, we can apply the Product Rule of Exponents by adding the exponents together while keeping the base the same.
So, we have 3^(5 + 7) as our next step.
Adding the exponents 5 and 7 gives us 3^12.
Therefore, the simplified expression is 3^12.
In summary, the Product Rule of Exponents allows us to add the exponents when multiplying exponential expressions with the same base. By applying this rule to 3^5⋅3^7, we simplify it to 3^12.
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, we can add the exponents.
Given the expression 3^5⋅3^7, we have the base 3 and two exponents, 5 and 7.
To simplify, we can apply the Product Rule of Exponents by adding the exponents together while keeping the base the same.
So, we have 3^(5 + 7) as our next step.
Adding the exponents 5 and 7 gives us 3^12.
Therefore, the simplified expression is 3^12.
In summary, the Product Rule of Exponents allows us to add the exponents when multiplying exponential expressions with the same base. By applying this rule to 3^5⋅3^7, we simplify it to 3^12.