Answer:
[tex]\frac{1}{625}[/tex]
Step-by-step explanation:
Given the indicinal equation;
[tex]{5^{-1} }*{5^{-3} }[/tex]
To multiply them, we will apply the multiplicative law of indices as shown where a, b, m and n can take any value;
[tex]a^{m} *a^{n} \\= a^{m+n}[/tex]
applying the formula to the given question;
[tex]{5^{-1} }*{5^{-3} }[/tex]
[tex]= 5^{-1+(-3)} \\= 5^{-1-3}\\ = 5^{-4} \\= \frac{1}{5^{4} } \\= \frac{1}{625}[/tex]
The product is [tex]\frac{1}{625}[/tex]
