Solve c^450-1 - Socratic AI (ScanMath)

Question

Simplify the expression

50 c^{4} - 1

Evaluate

c^{4} \times 50 - 1

Solution

50 c^{4} - 1

Show Solution

c_{1} = - \frac{4 5 0 ^{3}}{50}, c_{2} = \frac{4 5 0 ^{3}}{50}

Alternative Form

c_{1} \approx - 0.37606, c_{2} \approx 0.37606

Evaluate

c^{4} \times 50 - 1

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

c^{4} \times 50 - 1 = 0

Use the commutative property to reorder the terms

50 c^{4} - 1 = 0

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

50 c^{4} = 0 + 1

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

50 c^{4} = 1

Divide both sides

\frac{50 c ^{4}}{50} = \frac{1}{50}

Divide the numbers

c^{4} = \frac{1}{50}

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

c = \pm 4 \frac{1}{50}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{50}

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

\frac{4 1}{4 50}

Simplify the radical expression

\frac{1}{4 50}

Multiply by the Conjugate

\frac{4 5 0 ^{3}}{4 50 \times 4 5 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

450 \times 4 5 0^{3}

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

4 50 \times 5 0^{3}

Calculate the product

4 5 0^{4}

Reduce the index of the radical and exponent with 4

50

\frac{4 5 0 ^{3}}{50}

c = \pm \frac{4 5 0 ^{3}}{50}

Separate the equation into 2 possible cases

c = \frac{4 5 0 ^{3}}{50} c = - \frac{4 5 0 ^{3}}{50}

Solution

c_{1} = - \frac{4 5 0 ^{3}}{50}, c_{2} = \frac{4 5 0 ^{3}}{50}

Alternative Form

c_{1} \approx - 0.37606, c_{2} \approx 0.37606

Show Solution