Which rules of exponents will be used to evaluate this expression? check all that apply. product of powers
quotient of powers
power of a power
power of a product
negative exponent
zero exponent

We are given the expression:

Let us evaluate the expression step by step:

Step 1:

Power of a power: In this rule we multiply the powers 4 and (-5) in the numerator.

Step 2:

Quotient of power: Here we will subtract the power of denominator from numerator.

Step 3:

Negative exponent: Here we take reciprocal of what we got in step (2) , that will make the power positive.

We will use three rules as shown above .

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is