Question

Which of the following is equivalent to the radical expression below? 5^8*13

Answer 1

`(d)`
`5^(8.13) = 5^(8) * 5^{(1)/(10)} * 5^{(3)/(100)}`

Explanation:

Given

`5^(8.13)`

Required

Select an equivalent expression

`5^(8.13)`

Simplify the power

`5^(8.13) = 5^(8 + 0.1 + 0.03)`

Apply law of indices:

`5^(8.13) = 5^(8) * 5^(0.1) * 5^(0.03)`

Express decimal as fractions

`5^(8.13) = 5^(8) * 5^{(1)/(10)} * 5^{(3)/(100)}`