Question

Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.

12r^2t^8/8rt^5

Answer 1

-30y0

Answer 2

Evaluate the expression.
-3^2

Answer 3

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.

Answer 4

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.

Answer 5

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.