If (5^1/5)^5 = 25^x, then x = ?

  x = 1/2

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

__

  (5^(1/5))^5 = 25^x . . . . given

  5^(1/5×5) = (5^2)^x . . . . simplify left side, rewrite right side

  5^1 = 5^(2x) . . . . . . . . . simplify further

  1 = 2x . . . . . . . . . . . . . equate exponents of the same base

  x = 1/2 . . . . . . . . . . . divide by 2

_____

Additional comment

The Order of Operations tells you that exponentiation must be evaluated before multiplication or division. That means 5^1/5 is evaluated as ...

  (5^1)/5 = 5/5 = 1

If you want a fractional exponent, it must be put in parentheses: 5^(1/5). If you type your expression into the Go.ogle calculator, it will strictly adhere to the Order of Operations.

1)

(5^1/5)^5 = 25^(1/2) = 5

x =1/2

2) (8^1/3)^2 = 4^1 = 4

x = 1

ANSWER

1.

2.

QUESTION 1

The first sentence is .

Recall that;

We simplify the left hand side by applying this property to get;

.

.

We now rewrite the right hand side too in an index form to obtain;

We now equate the exponents to get;

.

.

QUESTION 2

The second sentence is

We simplify the left hand side first to get;

We now rewrite the left hand side too in index form to obtain;

We equate the exponents to get;

This implies that;

or

Hey!

I'll brake down every step (these steps wont have words, but if need any help, drop a comment)... And show you all the work, hope this helps...

Fractions Simplified

5 (1/5) > 26/5 > 5.2

8 (1/3) > 25/3 > 8.3333

First Problem

(5 1/5) 5 = 25x; x = ?

(5.2)*5 = 25x; x = ?

26 = 25x; x = ?

x = 26/25

x = 1.04

Second Problem

(8 1/3) 2 = 4x; x = ?

(8.3333)*2 = 4x; x = ?

16.66666 = 4x; x = ?

x = 16.66666/4

x = 4.166666

Estimated: x = 4.1667

ANSWER

1.

2.

QUESTION 1

The first sentence is .

Recall that;

We simplify the left hand side by applying this property to get;

.

.

We now rewrite the right hand side too in an index form to obtain;

We now equate the exponents to get;

.

.

QUESTION 2

The second sentence is

We simplify the left hand side first to get;

We now rewrite the left hand side too in index form to obtain;

We equate the exponents to get;

This implies that;

or

The expression used to represent g(x) as inverse of f(x) is

Option B is correct.

Step-by-step explanation:

We are given:

We need to find the expression that could be used to verify g(x) is the inverse of f(x).

We know that is inverse of function

So placing value of f(x) in g(x)

So, the expression used to represent g(x) as inverse of f(x) is

Option B is correct.

We can also solve to prove that

The point (56, 1.75) is on the line.

Step-by-step explanation:

Given two points, we can get the slope (m) as follows:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the points. Replacing with (8, 0.25) and (16, 0.5):

m = (0.5 - 0.25)/(16 - 8) = 0.03125

The point-slope form of a line is:

y - y1 = m(x - x1)

Replacing with data:

y - 0.25 = 0.03125(x - 8)

To know if point (56, 1.75) is on the line, we have to replace x = 56 in the obtained equation and check y-value, as follows:

y - 0.25 = 0.03125(56 - 8)

y - 0.25 = 1.5

y = 1.5 + 0.25 = 1.75

Then, the point is on the line. This means that there are 56 ounces in 1.75 quarts.

The point (56, 1.75) is on the line.

Step-by-step explanation:

Given two points, we can get the slope (m) as follows:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the points. Replacing with (8, 0.25) and (16, 0.5):

m = (0.5 - 0.25)/(16 - 8) = 0.03125

The point-slope form of a line is:

y - y1 = m(x - x1)

Replacing with data:

y - 0.25 = 0.03125(x - 8)

To know if point (56, 1.75) is on the line, we have to replace x = 56 in the obtained equation and check y-value, as follows:

y - 0.25 = 0.03125(56 - 8)

y - 0.25 = 1.5

y = 1.5 + 0.25 = 1.75

Then, the point is on the line. This means that there are 56 ounces in 1.75 quarts.