Question

$(125)^{\frac{2}{3}}\times(625)^{\frac{-1}{4}}=5^x$

x=?

 

• A. 1
• B. 11
• C. 5
• D. 9

Answer 1

Answer:

A. 1

$(5^3)^{\frac{2}{3}}\times(5^4)^{\frac{-1}{4}}=5^x$

$\because(x^m)^n=x^{mn}$

 

$(5^2)\times(5^-1)=5^x$

$\because{x^m\times{x^n}}=x^{m+n}$

$x=2-1=1$

$\because{x^m}=x^{n}\implies{m=n}$