For each sentence below, find the value of x that makes each sentence true. (5 ^1/5) ^5 = 25^x x = (8 ^1/3) ^2 = 4^ x x = ^a1

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

1)

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

x =1/2

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

x = 1

1)

2)

Step-by-step explanation:

We are asked to find value of x for each of our given expressions.

1).

Substitute :

Using exponent property , we will get:

We know when , then . Since base of both exponents is equal, so we can equate them as:

Therefore, the value of x is .

(2).

Using exponent property , we will get:

Substitute and 4 as Substitute :

Using exponent property , we will get:

We know when , then . Since base of both exponents is equal, so we can equate them as:

Therefore, the value of x is 1.

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