Express each of the following in the form
a)
b)

Explanation:​

Answers:

Each answer has 7 as the base and a fraction as an exponent.

==========================================================

Explanation:

One useful rule here is that . The fraction m/n is the exponent for the base x. Note how the index of the root (n) becomes the denominator of the fraction m/n. So for example if we had n = 3, then we'd be dealing with a cube root.

For part a), we have x = 7, m = 1 and n = 5 to get

-----------------

Part b) is the same idea

We would find that

Then apply the reciprocal to both sides. This is the same as raising both sides to the exponent -1

You could also use the rule that x^(-y) = 1/(x^y) when dealing with negative exponents.

In the second to last step shown above, I used the rule (x^y)^z = x^(y*z) on the right hand side.

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

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation