Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value. (-2)
1.
1-21-10
32
2. 21.24
-32
3.
32
1
4.
2-

1)

2)

3)

4)

Step-by-step explanation:

1)

Solving using exponent rule:

So,

2)

Using the exponent rule:

We have:

We also know that:

Using this rule:

So,

3)

Solving:

So,

4)

We know that:

So,

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.