Solve 5z^4z^2z-4z

Question

Simplify the expression

5 z^{7} - 4 z

Evaluate

5 z^{4} \times z^{2} \times z - 4 z

Solution

More Steps

Evaluate

5 z^{4} \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

5 z^{4 + 2 + 1}

Add the numbers

5 z^{7}

5 z^{7} - 4 z

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Factor the expression

z (5 z^{6} - 4)

Evaluate

5 z^{4} \times z^{2} \times z - 4 z

Multiply

More Steps

Evaluate

5 z^{4} \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

5 z^{4 + 2 + 1}

Add the numbers

5 z^{7}

5 z^{7} - 4 z

Rewrite the expression

z \times 5 z^{6} - z \times 4

Solution

z (5 z^{6} - 4)

Show Solution

Find the roots

z_{1} = - \frac{6 12500}{5}, z_{2} = 0, z_{3} = \frac{6 12500}{5}

Alternative Form

z_{1} \approx - 0.963492, z_{2} = 0, z_{3} \approx 0.963492

Evaluate

5 z^{4} \times z^{2} \times z - 4 z

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

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

Multiply

More Steps

Multiply the terms

5 z^{4} \times z^{2} \times z

Multiply the terms with the same base by adding their exponents

5 z^{4 + 2 + 1}

Add the numbers

5 z^{7}

5 z^{7} - 4 z = 0

Factor the expression

z (5 z^{6} - 4) = 0

Separate the equation into 2 possible cases

z = 0 5 z^{6} - 4 = 0

Solve the equation

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Evaluate

5 z^{6} - 4 = 0

Move the constant to the right-hand side and change its sign

5 z^{6} = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

5 z^{6} = 4

Divide both sides

\frac{5 z ^{6}}{5} = \frac{4}{5}

Divide the numbers

z^{6} = \frac{4}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

z = \pm 6 \frac{4}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{4}{5}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 4}{6 5}

Simplify the radical expression

\frac{3 2}{6 5}

Multiply by the Conjugate

\frac{3 2 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{3 2 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 12500}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 12500}{5}

z = \pm \frac{6 12500}{5}

Separate the equation into 2 possible cases

z = \frac{6 12500}{5} z = - \frac{6 12500}{5}

z = 0 z = \frac{6 12500}{5} z = - \frac{6 12500}{5}

Solution

z_{1} = - \frac{6 12500}{5}, z_{2} = 0, z_{3} = \frac{6 12500}{5}

Alternative Form

z_{1} \approx - 0.963492, z_{2} = 0, z_{3} \approx 0.963492

Show Solution