Answer:
[tex]\frac{1}{625}[/tex]
Step-by-step explanation:
The given expression is [tex](5^{-1})(5^{-3})[/tex]
Apply the product law of exponent: [tex]x^a\cdot x^b=x^{a+b}[/tex]
[tex](5^{-1})(5^{-3})\\\\=5^{-1+(-3)}\\\\=5^{-4}[/tex]
Now, apply the exponent rule: [tex]x^{-a}=\frac{1}{x^a}[/tex]
[tex]5^{-4}\\\\=\frac{1}{5^4}\\\\=\frac{1}{625}[/tex]
Therefore, the product of the given expression is [tex]\frac{1}{625}[/tex]
