Solve l^454-1 - ScanMath

Question

Simplify the expression

54 l^{4} - 1

Evaluate

l^{4} \times 54 - 1

Solution

54 l^{4} - 1

Show Solution

l_{1} = - \frac{4 5 4 ^{3}}{54}, l_{2} = \frac{4 5 4 ^{3}}{54}

Alternative Form

l_{1} \approx - 0.368894, l_{2} \approx 0.368894

Evaluate

l^{4} \times 54 - 1

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

l^{4} \times 54 - 1 = 0

Use the commutative property to reorder the terms

54 l^{4} - 1 = 0

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

54 l^{4} = 0 + 1

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

54 l^{4} = 1

Divide both sides

\frac{54 l ^{4}}{54} = \frac{1}{54}

Divide the numbers

l^{4} = \frac{1}{54}

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

l = \pm 4 \frac{1}{54}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{54}

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

\frac{4 1}{4 54}

Simplify the radical expression

\frac{1}{4 54}

Multiply by the Conjugate

\frac{4 5 4 ^{3}}{4 54 \times 4 5 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

454 \times 4 5 4^{3}

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

4 54 \times 5 4^{3}

Calculate the product

4 5 4^{4}

Reduce the index of the radical and exponent with 4

54

\frac{4 5 4 ^{3}}{54}

l = \pm \frac{4 5 4 ^{3}}{54}

Separate the equation into 2 possible cases

l = \frac{4 5 4 ^{3}}{54} l = - \frac{4 5 4 ^{3}}{54}

Solution

l_{1} = - \frac{4 5 4 ^{3}}{54}, l_{2} = \frac{4 5 4 ^{3}}{54}

Alternative Form

l_{1} \approx - 0.368894, l_{2} \approx 0.368894

Show Solution