Use the Product Rule of Exponents to simplify the expression 2^4⋅2^2
The Product Rule of Exponents states that for any positive numbers a and b, and any integers m and n, a^m * a^n = a^(m+n).
Applying the Product Rule to the expression 2^4 * 2^2, we add the exponents 4 and 2 to get:
2^(4+2)
Simplifying further, 4+2 equals 6, so we have:
2^6
Therefore, 2^4 * 2^2 simplifies to 2^6.
To simplify the expression 2^4 * 2^2 using the Product Rule of Exponents, we can combine the like bases (which is 2) and add the exponents.
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, you add the exponents.
So, in this case, we have 2^4 * 2^2.
Step 1: Add the exponents of the same base.
4 + 2 = 6
Step 2: Rewrite the expression with the new exponent.
2^6
Therefore, the simplified expression is 2^6.
To simplify the expression using the product rule of exponents, we can combine the exponents when multiplying powers with the same base.
The product rule states that for any non-zero number a and any integers m and n,
a^m * a^n = a^(m+n).
In this case, we have 2^4 * 2^2. Since the base (2) is the same, we can add the exponents.
Therefore, 2^4 * 2^2 = 2^(4+2).
Now, we can simplify the exponent:
2^(4+2) = 2^6.
Therefore, 2^4 * 2^2 simplifies to 2^6.