Question

which expression is equivalent to 10^{-1} cdot 10^{5}? 10^{4}, \frac{1}{10^{-5}}, \frac{1}{10^{4}}, 10^{-5}

Explanation:

Step1: Apply exponent - product rule

When multiplying two numbers with the same base \(a^m\cdot a^n=a^{m + n}\), here \(a = 10\), \(m=-1\) and \(n = 5\). So \(10^{-1}\cdot10^{5}=10^{-1 + 5}\).

Step2: Calculate the exponent

\(10^{-1+5}=10^{4}\).

Answer:

\(10^{4}\)