Solve L^6315-1 - ScanMath

Question

Simplify the expression

315 L^{6} - 1

Evaluate

L^{6} \times 315 - 1

Solution

315 L^{6} - 1

Show Solution

L_{1} = - \frac{6 31 5 ^{5}}{315}, L_{2} = \frac{6 31 5 ^{5}}{315}

Alternative Form

L_{1} \approx - 0.383367, L_{2} \approx 0.383367

Evaluate

L^{6} \times 315 - 1

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

L^{6} \times 315 - 1 = 0

Use the commutative property to reorder the terms

315 L^{6} - 1 = 0

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

315 L^{6} = 0 + 1

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

315 L^{6} = 1

Divide both sides

\frac{315 L ^{6}}{315} = \frac{1}{315}

Divide the numbers

L^{6} = \frac{1}{315}

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

L = \pm 6 \frac{1}{315}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{315}

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

\frac{6 1}{6 315}

Simplify the radical expression

\frac{1}{6 315}

Multiply by the Conjugate

\frac{6 31 5 ^{5}}{6 315 \times 6 31 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

6315 \times 6 31 5^{5}

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

6 315 \times 31 5^{5}

Calculate the product

6 31 5^{6}

Reduce the index of the radical and exponent with 6

315

\frac{6 31 5 ^{5}}{315}

L = \pm \frac{6 31 5 ^{5}}{315}

Separate the equation into 2 possible cases

L = \frac{6 31 5 ^{5}}{315} L = - \frac{6 31 5 ^{5}}{315}

Solution

L_{1} = - \frac{6 31 5 ^{5}}{315}, L_{2} = \frac{6 31 5 ^{5}}{315}

Alternative Form

L_{1} \approx - 0.383367, L_{2} \approx 0.383367

Show Solution