Solve 6k^3(k^2)-4

Question

Simplify the expression

6 k^{5} - 4

Evaluate

6 k^{3} \times k^{2} - 4

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

6 k^{3 + 2}

Add the numbers

6 k^{5}

6 k^{5} - 4

Show Solution

Factor the expression

2 (3 k^{5} - 2)

Evaluate

6 k^{3} \times k^{2} - 4

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

6 k^{3 + 2}

Add the numbers

6 k^{5}

6 k^{5} - 4

Solution

2 (3 k^{5} - 2)

Show Solution

Find the roots

k = \frac{5 162}{3}

Alternative Form

k \approx 0.922108

Evaluate

6 k^{3} (k^{2}) - 4

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

6 k^{3} (k^{2}) - 4 = 0

Calculate

6 k^{3} \times k^{2} - 4 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

6 k^{3 + 2}

Add the numbers

6 k^{5}

6 k^{5} - 4 = 0

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

6 k^{5} = 0 + 4

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

6 k^{5} = 4

Divide both sides

\frac{6 k ^{5}}{6} = \frac{4}{6}

Divide the numbers

k^{5} = \frac{4}{6}

Cancel out the common factor 2

k^{5} = \frac{2}{3}

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

5 k^{5} = 5 \frac{2}{3}

Calculate

k = 5 \frac{2}{3}

Solution

More Steps

Evaluate

5 \frac{2}{3}

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

\frac{5 2}{5 3}

Multiply by the Conjugate

\frac{5 2 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 2 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

52 \times 581

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

5 2 \times 81

Calculate the product

5162

\frac{5 162}{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{5 162}{3}

k = \frac{5 162}{3}

Alternative Form

k \approx 0.922108

Show Solution