Solve 64x^9 - 216

Question

Factor the expression

8 (2 x^{3} - 3) (4 x^{6} + 6 x^{3} + 9)

Evaluate

64 x^{9} - 216

Factor out 8 from the expression

8 (8 x^{9} - 27)

Solution

More Steps

Evaluate

8 x^{9} - 27

Rewrite the expression in exponential form

(2 x^{3})^{3} - 3^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(2 x^{3} - 3) ((2 x^{3})^{2} + 2 x^{3} \times 3 + 3^{2})

Evaluate

More Steps

Evaluate

(2 x^{3})^{2}

To raise a product to a power,raise each factor to that power

2^{2} (x^{3})^{2}

Evaluate the power

4 (x^{3})^{2}

Evaluate the power

4 x^{6}

(2 x^{3} - 3) (4 x^{6} + 2 x^{3} \times 3 + 3^{2})

Evaluate

(2 x^{3} - 3) (4 x^{6} + 6 x^{3} + 3^{2})

Evaluate

(2 x^{3} - 3) (4 x^{6} + 6 x^{3} + 9)

8 (2 x^{3} - 3) (4 x^{6} + 6 x^{3} + 9)

Show Solution

Find the roots

x = \frac{3 12}{2}

Alternative Form

x \approx 1.144714

Evaluate

64 x^{9} - 216

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

64 x^{9} - 216 = 0

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

64 x^{9} = 0 + 216

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

64 x^{9} = 216

Divide both sides

\frac{64 x ^{9}}{64} = \frac{216}{64}

Divide the numbers

x^{9} = \frac{216}{64}

Cancel out the common factor 8

x^{9} = \frac{27}{8}

Take the 9 -th root on both sides of the equation

9 x^{9} = 9 \frac{27}{8}

Calculate

x = 9 \frac{27}{8}

Solution

More Steps

Evaluate

9 \frac{27}{8}

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

\frac{9 27}{9 8}

Simplify the radical expression

More Steps

Evaluate

927

Write the number in exponential form with the base of 3

9 3^{3}

Reduce the index of the radical and exponent with 3

33

\frac{3 3}{9 8}

Simplify the radical expression

More Steps

Evaluate

98

Write the number in exponential form with the base of 2

9 2^{3}

Reduce the index of the radical and exponent with 3

32

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

\frac{3 12}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 12}{2}

x = \frac{3 12}{2}

Alternative Form

x \approx 1.144714

Show Solution