Solve f^2310e f-15

Question

Simplify the expression

310 e f^{3} - 15

Evaluate

f^{2} \times 310 e f - 15

Solution

More Steps

Evaluate

f^{2} \times 310 e f

Multiply the terms with the same base by adding their exponents

f^{2 + 1} \times 310 e

Add the numbers

f^{3} \times 310 e

Use the commutative property to reorder the terms

310 f^{3} e

Multiply the numbers

310 e f^{3}

310 e f^{3} - 15

Show Solution

Factor the expression

5 (62 e f^{3} - 3)

Evaluate

f^{2} \times 310 e f - 15

Multiply

More Steps

Evaluate

f^{2} \times 310 e f

Multiply the terms with the same base by adding their exponents

f^{2 + 1} \times 310 e

Add the numbers

f^{3} \times 310 e

Use the commutative property to reorder the terms

310 f^{3} e

Multiply the numbers

310 e f^{3}

310 e f^{3} - 15

Solution

5 (62 e f^{3} - 3)

Show Solution

Find the roots

f = \frac{3 11532 e ^{2}}{62 e}

Alternative Form

f \approx 0.261103

Evaluate

f^{2} \times 310 e f - 15

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

f^{2} \times 310 e f - 15 = 0

Multiply

More Steps

Multiply the terms

f^{2} \times 310 e f

Multiply the terms with the same base by adding their exponents

f^{2 + 1} \times 310 e

Add the numbers

f^{3} \times 310 e

Use the commutative property to reorder the terms

310 f^{3} e

Multiply the numbers

310 e f^{3}

310 e f^{3} - 15 = 0

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

310 e f^{3} = 0 + 15

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

310 e f^{3} = 15

Divide both sides

\frac{310 e f ^{3}}{310 e} = \frac{15}{310 e}

Divide the numbers

f^{3} = \frac{15}{310 e}

Cancel out the common factor 5

f^{3} = \frac{3}{62 e}

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

3 f^{3} = 3 \frac{3}{62 e}

Calculate

f = 3 \frac{3}{62 e}

Solution

More Steps

Evaluate

3 \frac{3}{62 e}

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

\frac{3 3}{3 62 e}

Multiply by the Conjugate

\frac{3 3 \times 3 6 2 ^{2} e ^{2}}{3 62 e \times 3 6 2 ^{2} e ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 6 2^{2} e^{2}

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

3 3 \times 6 2^{2} e^{2}

Calculate the product

3 11532 e^{2}

\frac{3 11532 e ^{2}}{3 62 e \times 3 6 2 ^{2} e ^{2}}

Multiply the numbers

More Steps

Evaluate

3 62 e \times 3 6 2^{2} e^{2}

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

3 62 e \times 6 2^{2} e^{2}

Calculate the product

3 6 2^{3} e^{3}

Calculate

62 e

\frac{3 11532 e ^{2}}{62 e}

f = \frac{3 11532 e ^{2}}{62 e}

Alternative Form

f \approx 0.261103

Show Solution