Given expression:
[tex]\frac{5^{-4}\times\text{ 5}^7}{5^3}[/tex]
To simplify the problem, we apply the laws of indices:
[tex]\begin{gathered} x^a\text{ }\times\text{ x}^b\text{ = x}^{a+b} \\ x^a\text{ }\div\text{ x}^b\text{ = x}^{a-b} \end{gathered}[/tex]
Hence, we have:
[tex]\begin{gathered} =\text{ }\frac{5^{-4+7}}{5^3} \\ =\text{ }\frac{5^3}{5^3} \\ =\text{ 5}^{3-3} \\ =\text{ 5}^0 \\ =1 \end{gathered}[/tex]
Answer : 1
