Question

For each sentence below, find the value of x that makes each sentence true.

(5 ^1/5) ^5 = 25^x x = ____^a0
(8 ^1/3) ^2 = 4^ x x = ____ ^a1

Answer 1

ANSWER

1. $x=\frac{1}{2}$

2. $x=1$

QUESTION 1

The first sentence is $(5^{\frac{1}{5}})^5=25^x$.

Recall that;

$(a^m)^n=a^{mn}$

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

$5^{\frac{1}{5}\times 5}=25^x$.

$\Rightarrow 5^{1}=25^x$.

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

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$.

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$.

QUESTION 2

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

$2^2=4^x$

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

$2^2=2^{2x}$

We equate the exponents to get;

$2=2x$

This implies that;

$1=x$

or

$x=1$

Answer 2

Answer:

It's 1/2 and then 1

Step-by-step explanation:

The answer above should have a 5-strar rating.  I chose 1/2 and 1 as the answer and I got it right.

Hope I helped:)

Have a great day!!!