Question

An equation containing a rational exponent is shown.

4x3/2 - 100 = 400

What is the value of x that makes the equation true?

Answer 1

x = 25

Explanation:

Given

4
`x^{(3)/(2) }` - 100 = 400 ( add 100 to both sides )

4
`x^{(3)/(2) }` = 500 ( divide both sides by 4 )

`x^{(3)/(2) }` = 125 ( square both sides )

x³ = 15625 (take the cube root of both sides )

x =
`\sqrt[3]{15625}` = 25

Answer 2

The value that makes the equation true is 25.

Explanation:

The given expression is

`4x^{(3)/(2) } -100=400`

We solve for
`x`

`4x^{(3)/(2) } -100=400\\4x^{(3)/(2) } =400+100\\4x^{(3)/(2) } =500\\x^{(3)/(2) } =(500)/(4)\\ x^{(3)/(2) } =125\\(x^{(3)/(2) })^{(2)/(3) } =(125)^{(2)/(3) } \\x=\sqrt[3]{125^(2) } =(\sqrt[3]{125} )^(2) \\x=5^(2)\\ x=25`

Therefore, the value that makes the equation true is 25.