Use the product, quotient, and power rules, as necessary, to simplify the following expression.
27
22
27 / (2 * 2) = 27 / 4 = 6.75
To simplify the expression 27/22 using the product, quotient, and power rules, we can begin by breaking down the numerator and denominator.
The numerator 27 can be written as (3^3), since 3 raised to the power of 3 equals 27.
The denominator 22 cannot be simplified further.
Now, we can evaluate 27/22 as a quotient.
(3^3) / 22
Next, we can simplify further by applying the power rule. Since we have an exponent in the numerator, we can divide the exponent by the denominator.
3^(3-2) / 22
Simplifying the exponent, we have:
3^1 / 22
Since any number raised to the power of 1 is itself, we can conclude that:
3 / 22
Therefore, the expression 27/22 simplifies to 3/22.
To simplify the expression 27^2/2^2, we will use the product, quotient, and power rules.
First, let's simplify the numerator, 27^2. This means we need to multiply 27 by itself.
27^2 = 27 * 27 = 729
Next, let's simplify the denominator, 2^2. This means we need to multiply 2 by itself.
2^2 = 2 * 2 = 4
So, the expression becomes 729/4.
Now, let's simplify this division. We divide the numerator by the denominator.
729/4 = 182.25
Therefore, the simplified expression is 182.25.