Question

Yara multiplies and divides a certain number by the same

Answer 1

For this case we have to:

x: Represents the unknown number

y: Represents the exponent of base 10

So, considering a system of equations we have:

$x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004$

From the first equation we have:

$10 ^ y = \frac {40,000} {x}$

Substituting in the second equation:

$\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}$

We choose the positive value:

$x = 0.4$

So, the number is 0.4.

So:

$10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5$

Thus, the exponent is 5.

Answer:

Yara use 0.4 and$10 ^ 5$