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:

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

Applying property A) in the given expression we get:

$(5^2)^4\times5^3=5^{2\cdot4}\times5^3=5^8\times5^3\text{.}$

Applying property B) in the above equation we get:

$5^8\times5^3=5^{8+3}=5^{11}\text{.}$

Therefore:

$(5^2)^4\times5^3=5^{11.}$

Answer:

$5^{11}\text{.}$