Solve e-l^31e^5 - ScanMath

Question

Simplify the expression

e - e^{5} l^{3}

Evaluate

e - l^{3} \times 1 \times e^{5}

Solution

More Steps

Evaluate

l^{3} \times 1 \times e^{5}

Rewrite the expression

l^{3} e^{5}

Use the commutative property to reorder the terms

e^{5} l^{3}

e - e^{5} l^{3}

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Factor the expression

e (1 - e^{4} l^{3})

Evaluate

e - l^{3} \times 1 \times e^{5}

Multiply the terms

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Evaluate

l^{3} \times 1 \times e^{5}

Rewrite the expression

l^{3} e^{5}

Use the commutative property to reorder the terms

e^{5} l^{3}

e - e^{5} l^{3}

Solution

e (1 - e^{4} l^{3})

Show Solution

Find the roots

l = \frac{3 e ^{2}}{e ^{2}}

Alternative Form

l \approx 0.263597

Evaluate

e - l^{3} \times 1 \times e^{5}

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

e - l^{3} \times 1 \times e^{5} = 0

Multiply the terms

More Steps

Multiply the terms

l^{3} \times 1 \times e^{5}

Rewrite the expression

l^{3} e^{5}

Use the commutative property to reorder the terms

e^{5} l^{3}

e - e^{5} l^{3} = 0

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

- e^{5} l^{3} = 0 - e

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

- e^{5} l^{3} = - e

Change the signs on both sides of the equation

e^{5} l^{3} = e

Divide both sides

\frac{e ^{5} l ^{3}}{e ^{5}} = \frac{e}{e ^{5}}

Divide the numbers

l^{3} = \frac{e}{e ^{5}}

Divide the numbers

l^{3} = \frac{1}{e ^{4}}

Take the 3 -th root on both sides of the equation

3 l^{3} = 3 \frac{1}{e ^{4}}

Calculate

l = 3 \frac{1}{e ^{4}}

Solution

More Steps

Evaluate

3 \frac{1}{e ^{4}}

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

\frac{3 1}{3 e ^{4}}

Simplify the radical expression

\frac{1}{3 e ^{4}}

Simplify the radical expression

More Steps

Evaluate

3 e^{4}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

3 e^{3 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

3 e^{3} \times e

The root of a product is equal to the product of the roots of each factor

3 e^{3} \times 3 e

Reduce the index of the radical and exponent with 3

e 3 e

\frac{1}{e 3 e}

Multiply by the Conjugate

\frac{3 e ^{2}}{e 3 e \times 3 e ^{2}}

Multiply the numbers

More Steps

Evaluate

e 3 e \times 3 e^{2}

Multiply the terms

e \times e

Multiply the terms with the same base by adding their exponents

e^{1 + 1}

Add the numbers

e^{2}

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

l = \frac{3 e ^{2}}{e ^{2}}

Alternative Form

l \approx 0.263597

Show Solution