Question

What is the relationship between ​ 2.57×10^4 ​ and ​ 2.57×10^−1 ​ ?

Select from the drop-down menus to correctly complete the statement.
​ 2.57×10^4 ​ is
times
than ​ 2.57×10^−1 ​ .

Answer 1

It is 10^-5 times than 2.57*10^-1

Answer 2

Answer:

The number $2.57\times 10^4$  is 10⁵ times of  $2.57\times 10^{-1}$.

Step-by-step explanation:

The first number is

$2.57\times 10^4$

The second number is

$2.57\times 10^{-1}$

Let  $2.57\times 10^4$  is x times of  $2.57\times 10^{-1}$.

$2.57\times 10^4=x\times 2.57\times 10^{-1}$

Divide both sides by  $2.57\times 10^{-1}$.

$\frac{2.57\times 10^4}{2.57\times 10^{-1}}=x$

$\frac{10^4}{10^{-1}}=x$

Use properties of exponent:

$\frac{a^m}{a^n}=a^{m-n}$

$10^{4-(-1)}=x$

$10^5=x$

Therefore the number $2.57\times 10^4$  is 10⁵ times of  $2.57\times 10^{-1}$.