Question

Which of the following is equivalent to the expression below? 5^8.13

Answer 1

Given:

`5^(8.13)`

Required:

We need to find the equlivale expression for the given expression.

Step-by-step explanation:

Consider the decimal value 8.13.

`8.13=8+0.1+0.03`

Recall that the first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place.

`0.1=(1)/(10)`
`0.03=(3)/(100)`
`8.13=8+(1)/(10)+(3)/(100)`

The given can be written as follows.

`5^(8.13)=5^{8+(1)/(10)+(3)/(100)}`
`\text{ Use }a^(n+m)=a^n\cdot a^m.`
`5^(8.13)=5^8\cdot5^{(1)/(10)}\cdot5^{(3)/(100)}`

Final answer:

`5^8\cdot5^{(1)/(10)}\cdot5^{(3)/(100)}`