Question

By multiplying ${\left(10\right)}^5$ by ${\left(10\right)}^{-10}$ we get _____. Fill in the blank to make the statement true.

Answer 1

${\left(10\right)}^5\times {\left(10\right)}^{-10}$

Using law of exponent, ${\left(a\right)}^m\times {\left(a\right)}^n={\left(a\right)}^{m+n}$, we get

$$\begin{gathered} {\left(10\right)}^5\times {\left(10\right)}^{-10} \\ ={\left(10\right)}^{5+(-10)} \\ ={\left(10\right)}^{5-10} \\ ={\left(10\right)}^{-5} \end{gathered}$$

Hence, By multiplying ${\left(10\right)}^{5}and{\left(10\right)}^{-10}$, we get ${\left(10\right)}^{-5}$.