Apply the Product Rule of Exponents to form an equivalent expression of 16⋅12⋅11 .(1 point)
Responses
13
1 cubed
113
1 superscript 13 baseline
112
1 superscript 12 baseline
19
112
To apply the product rule of exponents, we need to find the common base and add the exponents.
The expression 16⋅12⋅11 can be rewritten as (2^4)⋅(2^2⋅3)⋅(11).
To simplify this expression, we add the exponents of the common base 2:
(2^4)⋅(2^2⋅3)⋅(11) = 2^(4+2⋅3)⋅(11) = 2^10⋅(11).
Therefore, an equivalent expression for 16⋅12⋅11 using the product rule of exponents is 2^10⋅(11).
To apply the Product Rule of Exponents, you need to know the basic rule: when multiplying two numbers with the same base, you add their exponents. If we break down the expression 16⋅12⋅11, we can rewrite it using exponents:
16 = 2^4 (since 2^4 = 16)
12 = 2^2 * 3^1 (since 2^2 = 4 and 3^1 = 3)
11 = 11^1 (since any number raised to the power of 1 is itself)
Now, let's use the Product Rule of Exponents:
(2^4) * (2^2 * 3^1) * 11^1
When two numbers with the same base are multiplied, you add the exponents. So:
2^4 * 2^2 * 3^1 * 11^1 = 2^(4+2) * 3^1 * 11^1
Simplifying further:
2^(6) * 3^1 * 11^1 = 64 * 3 * 11 = 2112
So, the equivalent expression of 16⋅12⋅11 using the Product Rule of Exponents is 2112.