Question

The value of$(8^{-25}-8^{-26})$ is

• A. $7\times 8^{-25}$
• B. $7\times 8^{-26}$
• C. $8\times 8^{-26}$
• D. None of the above

Answer 1

The correct option is B

$7\times 8^{-26}$

:Find the value of$(8^{-25}-8^{-26})$:

$\begin{array}{rcl}(8^{-25}-8^{-26})& =& (8^{-25}-8^{-25}.8^{-1})\\ & =& 8^{-25}\left(1-8^{-1}\right)\\ & =& 8^{-25}\left(1-\frac{1}{8}\right)\left[\because {\mathrm{a}}^{-\mathrm{m}}=\frac{1}{{\mathrm{a}}^{\mathrm{m}}}\right]\\ & =& 8^{-25}\left(\frac{8-1}{8}\right)\\ & =& 8^{-25}\times \frac{7}{8}\\ & =& 8^{-25}\times 8^{-1}\times 7\\ & =& 7\times 8^{-26}\\ \therefore (8^{-25}-8^{-26})& =& 7\times 8^{-26}\end{array}$

$\therefore$Hence, the correct option is B.