Question

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

Answer 1

Given expression:

`\frac{5^(-4)*\text{ 5}^7}{5^3}`

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

`\begin{gathered} x^a\text{ }*\text{ x}^b\text{ = x}^(a+b) \\ x^a\text{ }/\text{ x}^b\text{ = x}^(a-b) \end{gathered}`

Hence, we have:

`\begin{gathered} =\text{ }(5^(-4+7))/(5^3) \\ =\text{ }(5^3)/(5^3) \\ =\text{ 5}^(3-3) \\ =\text{ 5}^0 \\ =1 \end{gathered}`

Answer : 1