Question

Find the value of the expression$\frac{{10}^{-1}\times 5^{x-3}\times 4^{x-1}}{10\times 5^{x-5}\times 4^{x-2}}$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$\frac{{10}^{-1}\times 5^{x-3}\times 4^{x-1}}{10\times 5^{x-5}\times 4^{x-2}}$ $={10}^{-1-1}\times 5^{(x-3)-(x-5)}\times 4^{(x-1)-(x-2)}$

$={10}^{-2}\times 5^{(x-3-x+5)}\times 4^{(x-1-x+2)}=\frac{1}{{10}^2}\times 5^2\times 4^1=\frac{100}{100}=1$