Question

Simplify and write the answer with positive exponents - (25/26)raised power -3 ÷ (25/26)raised power -5​

Answer 1

(25/26)^-3 ÷ (25/26)^-5 = (25/26)^-3-(-5)

= (25/26)^-3+5
= (25/26)² .......

Answer 2

Answer: (25/26)²

Step-by-step explanation:

Given,

$(\frac{25}{26})^{-3}\;\div\;(\frac{25}{26})^{-5}\\\;\\=(\frac{26}{25})^{3}\;\div\;(\frac{26}{25})^{5}\;\;\;\;\;\because(\frac{a}{b})^{-n}=(\frac{b}{a})^n\\\;\\=(\frac{26}{25})^3\times(\frac{25}{26})^5\\\;\\=\frac{26^3}{25^3}\times\frac{25^5}{26^5}\\\;\\=\frac{26^3}{26^5}\times\frac{25^5}{25^3}\\\;\\=(26)^{3-5}\times(25)^{5-3}\\\;\\=(26)^{-2}\times(25)^2\\\;\\=\frac{1}{26^2}\times\frac{25^2}{1}\\\;\\=\frac{25^2}{26^2}\\\;\\=(\frac{25}{26})^2$