What is the answer to 12x^5-384x^{10/3}=0 ?

The answer to 12x^5-384x^{10/3}=0 is x=0,x=8

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12x^5-384x^{10/3}=0

12 x^{5} - 384 x^{\frac{10}{3}} = 0

x = 0, x = 8

Solution steps

12 x^{5} - 384 x^{\frac{10}{3}} = 0

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{5} = (x^{\frac{1}{3}})^{(5 \cdot 3)}

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{10}{3}} = (x^{\frac{1}{3}})^{10}

12 (x^{\frac{1}{3}})^{15} - 384 (x^{\frac{1}{3}})^{10} = 0

Rewrite the equation with

x^{\frac{1}{3}} = u

12 u^{15} - 384 u^{10} = 0

Solve

12 u^{15} - 384 u^{10} = 0 : u = 0, u = 2

u = 0, u = 2

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

x^{\frac{1}{3}} = 0 : x = 0

Solve

x^{\frac{1}{3}} = 2 : x = 8

x = 0, x = 8

Verify Solutions:

x = 0

True

, x = 8

True

The solutions are

x = 0, x = 8

x + 7 + 3 = x - 4

2^{2} + x^{2} = 25

2 x - 4 + 2 = x

4 x + 8 + 1 = x

- 2 = - x + (4 x - 3)^{\frac{1}{2}}

What is the answer to 12x^5-384x^{10/3}=0 ?
The answer to 12x^5-384x^{10/3}=0 is x=0,x=8
Solve for x: 12x^5-384x^{10/3}=0
The solution is x=0,x=8