Solve z^2-16z^64 - ScanMath

Question

Simplify the expression

z^{2} - 64 z^{6}

Evaluate

z^{2} - 16 z^{6} \times 4

Solution

z^{2} - 64 z^{6}

Show Solution

z^{2} (1 - 8 z^{2}) (1 + 8 z^{2})

Evaluate

z^{2} - 16 z^{6} \times 4

Evaluate

z^{2} - 64 z^{6}

Factor out z^{2} from the expression

z^{2} (1 - 64 z^{4})

Solution

More Steps

Evaluate

1 - 64 z^{4}

Rewrite the expression in exponential form

1^{2} - (8 z^{2})^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(1 - 8 z^{2}) (1 + 8 z^{2})

z^{2} (1 - 8 z^{2}) (1 + 8 z^{2})

Show Solution

z_{1} = - \frac{2}{4}, z_{2} = 0, z_{3} = \frac{2}{4}

Alternative Form

z_{1} \approx - 0.353553, z_{2} = 0, z_{3} \approx 0.353553

Evaluate

z^{2} - 16 z^{6} \times 4

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

z^{2} - 16 z^{6} \times 4 = 0

Multiply the terms

z^{2} - 64 z^{6} = 0

Factor the expression

z^{2} (1 - 64 z^{4}) = 0

Separate the equation into 2 possible cases

z^{2} = 0 1 - 64 z^{4} = 0

The only way a power can be 0 is when the base equals 0

z = 0 1 - 64 z^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 64 z^{4} = 0

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

- 64 z^{4} = 0 - 1

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

- 64 z^{4} = - 1

Change the signs on both sides of the equation

64 z^{4} = 1

Divide both sides

\frac{64 z ^{4}}{64} = \frac{1}{64}

Divide the numbers

z^{4} = \frac{1}{64}

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

z = \pm 4 \frac{1}{64}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{64}

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

\frac{4 1}{4 64}

Simplify the radical expression

\frac{1}{4 64}

Simplify the radical expression

\frac{1}{2 2}

Multiply by the Conjugate

\frac{2}{2 2 \times 2}

Multiply the numbers

\frac{2}{4}

z = \pm \frac{2}{4}

Separate the equation into 2 possible cases

z = \frac{2}{4} z = - \frac{2}{4}

z = 0 z = \frac{2}{4} z = - \frac{2}{4}

Solution

z_{1} = - \frac{2}{4}, z_{2} = 0, z_{3} = \frac{2}{4}

Alternative Form

z_{1} \approx - 0.353553, z_{2} = 0, z_{3} \approx 0.353553

Show Solution