Q60. - Algebra 2

Question

Determine which is greater ${100}^{10}\text{\hspace{0.17em}or }{10}^{100}$ . Explain.

Step-by-Step Solution

Answer

The greater number is ${10}^{100}$ .

Step 1. Write down the given information.

The given numbers are ${100}^{10}\text{\hspace{0.17em}or }{10}^{100}$ .

Step 2. Comparing given numbers by reducing to same base.

The two numbers are compared by changing  ${100}^{10}$ to base 10.

$\begin{array}{c}{100}^{10}={\left({10}^2\right)}^{10}\\ ={\left(10\right)}^{2\times 10}\\ ={10}^{20}\\ <{10}^{100}\end{array}$

Hence,    ${10}^{100}>{100}^{10}$

Step 3. Conclusion.

The greater number is ${10}^{100}$ .