Question

Which expression is equivalent to (4(5^3)1/2?

Answer 1

`10√(5)`

Explanation:

In this problem, we are given expression in exponent form and we have to simplify the expression.

The expression is
`[4(5^(3) )]^{(1)/(2) }`

Now, we know that
`5^(3) = 5 * 5 * 5 = 125`

So,
`4(5^(3) ) = 4 * 125 = 500`

Now, 500 can be written as 100 × 5 = 10² × 5

Therefore,
`[4(5^(3) )]^{(1)/(2) } = (500)^{(1)/(2) } = 10√(5)` {Since 500 = 100 × 5 = 10² × 5} (Answer)