Use the Product Rule of Exponents to simplify the expression 2^4
• 2^2
The Product Rule of Exponents states that when you multiply two expressions that have the same base, you can add the exponents. In the case of 2^4 * 2^2, you have:
2^4 * 2^2 = 2^(4+2) = 2^6
Now, calculating 2^6 gives you:
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
So, 2^4 * 2^2 simplifies to 64.
Wrong
I apologize for any confusion. The explanation I provided is correct and based on the Product Rule of Exponents. Let's review it:
If you have two exponents with the same base being multiplied together like a^m * a^n, the Product Rule of Exponents states you add the exponents together while keeping the same base, so it becomes:
a^(m+n)
Applying this rule to your expression 2^4 * 2^2:
2^4 * 2^2 = 2^(4+2) = 2^6
To find the value of 2^6:
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
Therefore, 2^4 * 2^2 simplifies to 2^6, which calculates to 64. This is the correct application of the Product Rule of Exponents and the correct calculation for the expression you have provided. If there has been a misunderstanding or if you were expecting a different aspect of the problem to be addressed, please provide more information so I can assist you accordingly.
To simplify the expression 2^4 * 2^2 using the Product Rule of Exponents, we need to multiply the base (2 in this case) and add the exponents.
The Product Rule states that when multiplying two expressions with the same base, you keep the base and add the exponents. In this case, the base is 2.
So, with 2^4 * 2^2, we keep the base 2 and add the exponents 4 and 2:
2^(4+2)
Adding the exponents, we get:
2^6
Therefore, 2^4 * 2^2 simplifies to 2^6.