Solve k^6268-36 - ScanMath

Question

Simplify the expression

268 k^{6} - 36

Evaluate

k^{6} \times 268 - 36

Solution

268 k^{6} - 36

Show Solution

4 (67 k^{6} - 9)

Evaluate

k^{6} \times 268 - 36

Use the commutative property to reorder the terms

268 k^{6} - 36

Solution

4 (67 k^{6} - 9)

Show Solution

k_{1} = - \frac{6 9 \times 6 7 ^{5}}{67}, k_{2} = \frac{6 9 \times 6 7 ^{5}}{67}

Alternative Form

k_{1} \approx - 0.71564, k_{2} \approx 0.71564

Evaluate

k^{6} \times 268 - 36

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

k^{6} \times 268 - 36 = 0

Use the commutative property to reorder the terms

268 k^{6} - 36 = 0

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

268 k^{6} = 0 + 36

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

268 k^{6} = 36

Divide both sides

\frac{268 k ^{6}}{268} = \frac{36}{268}

Divide the numbers

k^{6} = \frac{36}{268}

Cancel out the common factor 4

k^{6} = \frac{9}{67}

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

k = \pm 6 \frac{9}{67}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{67}

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

\frac{6 9}{6 67}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{3 3}{6 67}

Multiply by the Conjugate

\frac{3 3 \times 6 6 7 ^{5}}{6 67 \times 6 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

33 \times 6 6 7^{5}

Use n a = mn a^{m} to expand the expression

6 3^{2} \times 6 6 7^{5}

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

6 3^{2} \times 6 7^{5}

Calculate the product

6 9 \times 6 7^{5}

\frac{6 9 \times 6 7 ^{5}}{6 67 \times 6 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

667 \times 6 6 7^{5}

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

6 67 \times 6 7^{5}

Calculate the product

6 6 7^{6}

Reduce the index of the radical and exponent with 6

67

\frac{6 9 \times 6 7 ^{5}}{67}

k = \pm \frac{6 9 \times 6 7 ^{5}}{67}

Separate the equation into 2 possible cases

k = \frac{6 9 \times 6 7 ^{5}}{67} k = - \frac{6 9 \times 6 7 ^{5}}{67}

Solution

k_{1} = - \frac{6 9 \times 6 7 ^{5}}{67}, k_{2} = \frac{6 9 \times 6 7 ^{5}}{67}

Alternative Form

k_{1} \approx - 0.71564, k_{2} \approx 0.71564

Show Solution