Solve z^432-4 - ScanMath

Question

Simplify the expression

32 z^{4} - 4

Evaluate

z^{4} \times 32 - 4

Solution

32 z^{4} - 4

Show Solution

4 (8 z^{4} - 1)

Evaluate

z^{4} \times 32 - 4

Use the commutative property to reorder the terms

32 z^{4} - 4

Solution

4 (8 z^{4} - 1)

Show Solution

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

Alternative Form

z_{1} \approx - 0.594604, z_{2} \approx 0.594604

Evaluate

z^{4} \times 32 - 4

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

z^{4} \times 32 - 4 = 0

Use the commutative property to reorder the terms

32 z^{4} - 4 = 0

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

32 z^{4} = 0 + 4

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

32 z^{4} = 4

Divide both sides

\frac{32 z ^{4}}{32} = \frac{4}{32}

Divide the numbers

z^{4} = \frac{4}{32}

Cancel out the common factor 4

z^{4} = \frac{1}{8}

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

z = \pm 4 \frac{1}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8}

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

\frac{4 1}{4 8}

Simplify the radical expression

\frac{1}{4 8}

Multiply by the Conjugate

\frac{4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4 8^{3}

The product of roots with the same index is equal to the root of the product

4 8 \times 8^{3}

Calculate the product

4 8^{4}

Transform the expression

4 2^{12}

Reduce the index of the radical and exponent with 4

2^{3}

\frac{2 ^{2} 4 2}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{4 2}{2}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

z_{1} \approx - 0.594604, z_{2} \approx 0.594604

Show Solution