what is the product of $(5^{-1})(5^{-3})$?\n$\frac{1}{625}$\n$\frac{1}{25}$\n25\n125
what is the product of $(5^{-1})(5^{-3})$?\n$\frac{1}{625}$\n$\frac{1}{25}$\n25\n125
Answer
Explanation:
Step1: Use exponent - product rule
When multiplying two numbers with the same base (a^m\times a^n=a^{m + n}), here (a = 5), (m=-1) and (n=-3). So (5^{-1}\times5^{-3}=5^{-1+( - 3)}=5^{-4}).
Step2: Use negative - exponent rule
The negative - exponent rule states that (a^{-n}=\frac{1}{a^{n}}). For (a = 5) and (n = 4), (5^{-4}=\frac{1}{5^{4}}).
Step3: Calculate (5^{4})
(5^{4}=5\times5\times5\times5 = 625). So (\frac{1}{5^{4}}=\frac{1}{625}).
Answer:
A. (\frac{1}{625})