Solve (4x-8)(16x^232x^64)

Question

Simplify the expression

8192 x^{9} - 16384 x^{8}

Evaluate

(4 x - 8) (16 x^{2} \times 32 x^{6} \times 4)

Remove the parentheses

(4 x - 8) \times 16 x^{2} \times 32 x^{6} \times 4

Multiply the terms

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Evaluate

16 \times 32 \times 4

Multiply the terms

512 \times 4

Multiply the numbers

2048

(4 x - 8) \times 2048 x^{2} \times x^{6}

Multiply the terms with the same base by adding their exponents

(4 x - 8) \times 2048 x^{2 + 6}

Add the numbers

(4 x - 8) \times 2048 x^{8}

Multiply the terms

2048 x^{8} (4 x - 8)

Apply the distributive property

2048 x^{8} \times 4 x - 2048 x^{8} \times 8

Multiply the terms

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Evaluate

2048 x^{8} \times 4 x

Multiply the numbers

8192 x^{8} \times x

Multiply the terms

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Evaluate

x^{8} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{8 + 1}

Add the numbers

x^{9}

8192 x^{9}

8192 x^{9} - 2048 x^{8} \times 8

Solution

8192 x^{9} - 16384 x^{8}

Show Solution

Factor the expression

8192 x^{8} (x - 2)

Evaluate

(4 x - 8) (16 x^{2} \times 32 x^{6} \times 4)

Remove the parentheses

(4 x - 8) \times 16 x^{2} \times 32 x^{6} \times 4

Multiply

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Multiply the terms

16 x^{2} \times 32 x^{6} \times 4

Multiply the terms

More Steps

Evaluate

16 \times 32 \times 4

Multiply the terms

512 \times 4

Multiply the numbers

2048

2048 x^{2} \times x^{6}

Multiply the terms with the same base by adding their exponents

2048 x^{2 + 6}

Add the numbers

2048 x^{8}

(4 x - 8) \times 2048 x^{8}

Multiply the terms

2048 x^{8} (4 x - 8)

Factor the expression

2048 x^{8} \times 4 (x - 2)

Solution

8192 x^{8} (x - 2)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2

Evaluate

(4 x - 8) (16 x^{2} \times 32 x^{6} \times 4)

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

(4 x - 8) (16 x^{2} \times 32 x^{6} \times 4) = 0

Multiply

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Multiply the terms

16 x^{2} \times 32 x^{6} \times 4

Multiply the terms

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Evaluate

16 \times 32 \times 4

Multiply the terms

512 \times 4

Multiply the numbers

2048

2048 x^{2} \times x^{6}

Multiply the terms with the same base by adding their exponents

2048 x^{2 + 6}

Add the numbers

2048 x^{8}

(4 x - 8) \times 2048 x^{8} = 0

Multiply the terms

2048 x^{8} (4 x - 8) = 0

Elimination the left coefficient

x^{8} (4 x - 8) = 0

Separate the equation into 2 possible cases

x^{8} = 0 4 x - 8 = 0

The only way a power can be 0 is when the base equals 0

x = 0 4 x - 8 = 0

Solve the equation

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Evaluate

4 x - 8 = 0

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

4 x = 0 + 8

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

4 x = 8

Divide both sides

\frac{4 x}{4} = \frac{8}{4}

Divide the numbers

x = \frac{8}{4}

Divide the numbers

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Evaluate

\frac{8}{4}

Reduce the numbers

\frac{2}{1}

Calculate

2

x = 2

x = 0 x = 2

Solution

x_{1} = 0, x_{2} = 2

Show Solution