Solve z^608-1 - ScanMath

Question

Simplify the expression

8 z^{6} - 1

Evaluate

z^{6} \times 8 - 1

Solution

8 z^{6} - 1

Show Solution

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

Evaluate

z^{6} \times 8 - 1

Use the commutative property to reorder the terms

8 z^{6} - 1

Rewrite the expression in exponential form

(2 z^{2})^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(2 z^{2} - 1) ((2 z^{2})^{2} + 2 z^{2} \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(2 z^{2})^{2}

To raise a product to a power,raise each factor to that power

2^{2} (z^{2})^{2}

Evaluate the power

4 (z^{2})^{2}

Evaluate the power

More Steps

Evaluate

(z^{2})^{2}

Multiply the exponents

z^{2 \times 2}

Multiply the terms

z^{4}

4 z^{4}

(2 z^{2} - 1) (4 z^{4} + 2 z^{2} \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

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

Solution

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

Show Solution

z_{1} = - \frac{2}{2}, z_{2} = \frac{2}{2}

Alternative Form

z_{1} \approx - 0.707107, z_{2} \approx 0.707107

Evaluate

z^{6} \times 8 - 1

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

z^{6} \times 8 - 1 = 0

Use the commutative property to reorder the terms

8 z^{6} - 1 = 0

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

8 z^{6} = 0 + 1

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

8 z^{6} = 1

Divide both sides

\frac{8 z ^{6}}{8} = \frac{1}{8}

Divide the numbers

z^{6} = \frac{1}{8}

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

z = \pm 6 \frac{1}{8}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{8}

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

\frac{6 1}{6 8}

Simplify the radical expression

\frac{1}{6 8}

Simplify the radical expression

More Steps

Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

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

Separate the equation into 2 possible cases

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

Solution

z_{1} = - \frac{2}{2}, z_{2} = \frac{2}{2}

Alternative Form

z_{1} \approx - 0.707107, z_{2} \approx 0.707107

Show Solution