Question

Simplify the following expression. Enter your answer in the form a^b.(5^2)^4 x 5^3=____

Answer 1

To solve this question we will use the following properties:

`\begin{gathered} A)\text{ (}a^m\text{)}^n=a^(m* n), \\ B)a^m* a^n=a^(m+n)\text{.} \end{gathered}`

Applying property A) in the given expression we get:

`(5^2)^4*5^3=5^(2\cdot4)*5^3=5^8*5^3\text{.}`

Applying property B) in the above equation we get:

`5^8*5^3=5^(8+3)=5^(11)\text{.}`

Therefore:

`(5^2)^4*5^3=5^(11.)`

Answer:

`5^(11)\text{.}`