Solve 5z(2z^3)^(-1/4)-5(2z^3)^(3/4)

Question

Simplify the expression

\frac{5 4 8 z - 10 z ^{2} 4 8 z}{2}

Show Solution

z = \frac{8 128}{2}

Alternative Form

z \approx 0.917004

Evaluate

5 z (2 z^{3})^{(- 1) \div 4} - 5 (2 z^{3})^{3 \div 4}

To find the roots of the expression,set the expression equal to 0

5 z (2 z^{3})^{(- 1) \div 4} - 5 (2 z^{3})^{3 \div 4} = 0

Find the domain

More Steps

5 z (2 z^{3})^{(- 1) \div 4} - 5 (2 z^{3})^{3 \div 4} = 0, z > 0

Calculate

5 z (2 z^{3})^{(- 1) \div 4} - 5 (2 z^{3})^{3 \div 4} = 0

Divide the numbers

5 z (2 z^{3})^{- 0.25} - 5 (2 z^{3})^{3 \div 4} = 0

Divide the numbers

5 z (2 z^{3})^{- 0.25} - 5 (2 z^{3})^{0.75} = 0

Convert the decimal into a fraction

More Steps

5 z (2 z^{3})^{- \frac{1}{4}} - 5 (2 z^{3})^{0.75} = 0

Convert the decimal into a fraction

More Steps

5 z (2 z^{3})^{- \frac{1}{4}} - 5 (2 z^{3})^{\frac{3}{4}} = 0

Multiply the terms

More Steps

\frac{5 4 8}{2} z^{\frac{1}{4}} - 5 (2 z^{3})^{\frac{3}{4}} = 0

Multiply the terms

\frac{5 4 8}{2} z^{\frac{1}{4}} - 5 4 2^{3} \times z^{\frac{9}{4}} = 0

Evaluate the power

\frac{5 4 8}{2} z^{\frac{1}{4}} - 548 \times z^{\frac{9}{4}} = 0

Factor the expression

z^{\frac{1}{4}} (\frac{5 4 8}{2} - 548 \times z^{8}) = 0

Separate the equation into 2 possible cases

z^{\frac{1}{4}} = 0 \frac{5 4 8}{2} - 548 \times z^{8} = 0

Solve the equation

z = 0 \frac{5 4 8}{2} - 548 \times z^{8} = 0

Solve the equation

More Steps

z = 0 z = \frac{8 128}{2} z = - \frac{8 128}{2}

Check if the solution is in the defined range

z = 0 z = \frac{8 128}{2} z = - \frac{8 128}{2}, z > 0

Solution

z = \frac{8 128}{2}

Alternative Form

z \approx 0.917004

Show Solution