Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.
12r^2t^8/8rt^5
To simplify the expression 12r^2t^8/8rt^5, we can apply the commutative and associative properties of real numbers and the properties of exponents.
First, let's use the commutative property to rearrange the terms in the numerator:
12r^2t^8 = 12t^8r^2
Next, we can use the associative property to group the terms in the numerator:
12t^8r^2 = (12t^8)(r^2)
Now, let's simplify the expression within the parentheses:
12t^8r^2 = (12)(t^8)(r^2)
Finally, let's use the properties of exponents to simplify the expression further:
(12)(t^8)(r^2) = 12t^(8-1)r^(2-1) = 12t^7r
Therefore, the simplified expression is 12t^7r.
To simplify the expression 12r^2t^8/8rt^5, we can apply the commutative and associative properties of real numbers as well as the properties of exponents.
First, let's simplify the numerical coefficients using the commutative property of multiplication. Rearranging the expression, we have:
(12/8) * (r^2/r) * (t^8/t^5)
Next, simplify each individual term using the properties of exponents:
12/8 = 3/2
(r^2/r) = r^(2-1) = r^1 = r
(t^8/t^5) = t^(8-5) = t^3
Now, we can substitute these simplified values back into the expression:
(3/2) * r * t^3
Finally, we can multiply the coefficients together:
(3/2) * r = (3r)/2
Therefore, the simplified expression becomes (3r/2) * t^3.
-30y0
The expression -30y^0 can be simplified as follows:
The property of any number raised to the power of 0 is equal to 1. Therefore, y^0 = 1.
Substituting this value into the expression, we have:
-30y^0 = -30(1) = -30
So, the simplified expression is -30.
Evaluate the expression.
-3^2
To evaluate the expression -3^2, we need to follow the order of operations, which states that we should perform any exponentiation before any multiplication or negation.
First, we must square the number 3.
3^2 = 3 * 3 = 9
Then, we apply the negative sign to the result:
-3^2 = -9
Therefore, the value of the expression -3^2 is -9.