Question

If $(x^{5/4})^x=(x^x)^{5/4}$ find x

• A. 5/4
• B. 25/16
• C. 625/256
• D. 4/5

Answer 1

Answer:

C. 625/256

$(x^{5/4})^x=(x^{x^{5/4}})$

$(x^{5/4\times{x}})=(x^{x^{5/4}})$

$x^{5x/4}=(x^{x^{5/4}})$

$5x/4=x^{5/4}$

$5x/4=x^{1+1/4}$

$5x/4=x^1\times{x^{1/4}}$

$5/4=x^{1/4}$

$x=(5/4)^4$

$x=625/256$