Given:
The given expression is [tex]5^{3 x} \cdot 5^{x+4} \cdot 5^{-3 x-1}[/tex]
We need to simplify the given expression.
Simplification:
Let us use the exponent rule to simplify the given expression.
Let us apply the exponent rule, [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex]
Thus, we have;
[tex]5^{3 x} \cdot 5^{x+4} \cdot 5^{-3 x-1}=5^{3 x+x+4-3 x-1}[/tex]
Now, we shall simplify the numerator.
The numerator of the expression can be simplified by adding the like terms.
Thus, we have;
[tex]5^{3 x} \cdot 5^{x+4} \cdot 5^{-3 x-1}=5^{x+3}[/tex]
Thus, the simplified value of the given expression is [tex]5^{x+3}[/tex]
