Question

An equation containing a rational exponent is shown.

Answer 1

Answer:

x = 25

Step-by-step explanation:

Given

4$x^{\frac{3}{2} }$ - 100 = 400 ( add 100 to both sides )

4$x^{\frac{3}{2} }$ = 500 ( divide both sides by 4 )

$x^{\frac{3}{2} }$ = 125 ( square both sides )

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

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

Answer 2

Answer:

The value that makes the equation true is 25.

Step-by-step explanation:

The given expression is

$4x^{\frac{3}{2} } -100=400$

We solve for $x$

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

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