We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
256
3
avatar

There are two numbers whose 400th powers are equal to 9^1000. In other words, there are two numbers that can replace x in the equation x^400 = 9^1000 making the equation true. What are those numbers? Explain the process by which you got your answer.

 Jun 24, 2019
 #1
avatar+8810 
+4

\(x^{400}\ =\ 9^{1000}\)

                              Take the  200th root of both sides of the equation.

\(x^{\frac{400}{200}}\ =\ 9^{\frac{1000}{200}}\)

 

\(x^{2}\ =\ 9^{5}\)

                              Take the ± sqrt of both sides. (We could have taken the 400th root of both sides to start with.)

\(x\ =\ \pm\sqrt{9^5}\)

                              Rewrite  95  as  310

\(x\ =\ \pm\sqrt{3^{10}}\)

 

\(x\ =\ \pm3^5\)

 

\(x\ =\ \pm243\)

.
 Jun 24, 2019
 #2
avatar+104962 
+2

Well....since it looks as though we're all at the same picnic.....here's my attempt at a weak answer

 

x^400 = 9^1000

 

Take the GCF of 400, 1000  = 200  ....so we can write

 

(x^2)^200 = (9^5)^200        take the 200th root of both sides

 

(x^2) = 9^5      and we can write

 

(x^2) = (3^2)^5

 

x^2  = 3^10      take both roots

 

x = ± √[3^10]  =   ± [ 3] ^(10/2)  =  ± [3]^5  =  ± 243

 

 

cool cool cool

 Jun 24, 2019
 #3
avatar+23354 
+2

There are two numbers whose 400th powers are equal to 9^1000.

In other words, there are two numbers that can replace x in the equation \(x^{400} = 9^{1000}\) making the equation true.
What are those numbers?

 

\(\begin{array}{|rcll|} \hline \mathbf{x^{400}} &=& \mathbf{9^{1000}} \quad | \quad \text{Take the 400th root of both sides } \\ x^{\frac{400}{400}} &=& 9^{\frac{1000}{400}} \\ x &=& 9^{\frac{5}{2}} \\ x &=& \sqrt{9^5} \\ \mathbf{ x} &=& \mathbf{\pm 243} \\ \hline \end{array}\)

 

laugh

 Jun 24, 2019

4 Online Users