Question

find the value of (5 ^-4 times 5 ^7)/5^3 in the simplest form

Answer 1

Given expression:

$\frac{5^{-4}\times\text{ 5}^7}{5^3}$

To simplify the problem, we apply the laws of indices:

$\begin{gathered} x^a\text{ }\times\text{ x}^b\text{ = x}^{a+b} \\ x^a\text{ }\div\text{ x}^b\text{ = x}^{a-b} \end{gathered}$

Hence, we have:

$\begin{gathered} =\text{ }\frac{5^{-4+7}}{5^3} \\ =\text{ }\frac{5^3}{5^3} \\ =\text{ 5}^{3-3} \\ =\text{ 5}^0 \\ =1 \end{gathered}$

Answer : 1