Which expression is equivalent to (x^4/3 x^2/3)^1/3?

Step-by-step explanation:

We have several properties of exponents in use here. The two that are used are:

(Exponents with the same base that are being multiplied together can have the exponents added)

(A base raised to a power, and then raised to another power means that you can multiply the exponents to get the same result as doing inside operations and then outside operations)

Let's apply it!

First, let's simplify what's inside the parenthesis.

(Remember, they have the same base of "x", so we can add the exponents)

= =

Now we have . Let's use the second rule.

=

Hope this helps! :^)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).