Question

Simplify. Note: For any value, your final answer must be a number. For any variable, the answer can be written in exponential form.

Answer 1

To simplify the expression you can use the following exponent rule:

`a^m\cdot a^n=a^(m+n)`

and the commutative property of multiplication:

`\begin{gathered} a\cdot b=b\cdot a \\ \text{ This Means that you can multiply in any order} \end{gathered}`

Then, you have

`\begin{gathered} \text{ Apply the commutative property} \\ 5^3\cdot\: x^2\cdot\: x^(-3)\cdot5^3\cdot\: x^4=5^3\cdot\: 5^3\cdot x^2\cdot\: x^(-3)\cdot\: x^4 \\ \text{ Apply the rule of exponents shown above} \\ 5^3\cdot\: x^2\cdot\: x^(-3)\cdot5^3\cdot\: x^4=5^(3+3)\cdot x^(2-3+4) \\ 5^3\cdot\: x^2\cdot\: x^(-3)\cdot5^3\cdot\: x^4=5^6\cdot x^3 \\ 5^3\cdot\: x^2\cdot\: x^(-3)\cdot5^3\cdot\: x^4=15625x^3 \end{gathered}`

Therefore, the simplified expression is

`15625x^3`