Solve 16-6k^4k-14

Question

Simplify the expression

2 - 6 k^{5}

Evaluate

16 - 6 k^{4} \times k - 14

Multiply

More Steps

Multiply the terms

- 6 k^{4} \times k

Multiply the terms with the same base by adding their exponents

- 6 k^{4 + 1}

Add the numbers

- 6 k^{5}

16 - 6 k^{5} - 14

Solution

2 - 6 k^{5}

Show Solution

Factor the expression

2 (1 - 3 k^{5})

Evaluate

16 - 6 k^{4} \times k - 14

Multiply

More Steps

Multiply the terms

6 k^{4} \times k

Multiply the terms with the same base by adding their exponents

6 k^{4 + 1}

Add the numbers

6 k^{5}

16 - 6 k^{5} - 14

Subtract the numbers

2 - 6 k^{5}

Solution

2 (1 - 3 k^{5})

Show Solution

Find the roots

k = \frac{5 81}{3}

Alternative Form

k \approx 0.802742

Evaluate

16 - 6 k^{4} \times k - 14

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

16 - 6 k^{4} \times k - 14 = 0

Multiply

More Steps

Multiply the terms

6 k^{4} \times k

Multiply the terms with the same base by adding their exponents

6 k^{4 + 1}

Add the numbers

6 k^{5}

16 - 6 k^{5} - 14 = 0

Subtract the numbers

2 - 6 k^{5} = 0

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

- 6 k^{5} = 0 - 2

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

- 6 k^{5} = - 2

Change the signs on both sides of the equation

6 k^{5} = 2

Divide both sides

\frac{6 k ^{5}}{6} = \frac{2}{6}

Divide the numbers

k^{5} = \frac{2}{6}

Cancel out the common factor 2

k^{5} = \frac{1}{3}

Take the 5 -th root on both sides of the equation

5 k^{5} = 5 \frac{1}{3}

Calculate

k = 5 \frac{1}{3}

Solution

More Steps

Evaluate

5 \frac{1}{3}

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

\frac{5 1}{5 3}

Simplify the radical expression

\frac{1}{5 3}

Multiply by the Conjugate

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

Simplify

\frac{5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

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

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{5 81}{3}

k = \frac{5 81}{3}

Alternative Form

k \approx 0.802742

Show Solution