Question

The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced 3 times. Write the voltage in exponential form. What was the original voltage in the circuit.

Answer 1

Answer: (3/5)^3 in exponential form and 3/5 a volt

Explanation:

Answer 2

The voltage in exponential form would be
`((3)/(5))^3`.

The original voltage in the circuit is
`(3)/(5)` of a volt.

Explanation:

Let x represent the original voltage.

We have been given that the voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced 3 times.

The original voltage multiplied by itself for 3 times would be
`x\cdot x\cdot x=x^3`.

Now, we will equate
`x^3` with 27/125 as:

`x^3=(27)/(125)`

We know that 27 is cube of 3 and 125 is cube of 5, so we can represent our equation as:

`x^3=(3^3)/(5^3)`

`x^3=((3)/(5))^3`

Therefore, the voltage in exponential form would be
`((3)/(5))^3`

Now, we will take cube root of both sides to find original voltage in the circuit as:

`\sqrt[3]{x^3} =\sqrt[3]{((3)/(5))^3}`

Using property
`\sqrt[n]{a^n} =a`, we will get:

`x =(3)/(5)`

Therefore, the original voltage in the circuit is
`(3)/(5)` of a volt.