Solve \frac{(x 8)(x^6) 4}{(x 8)(x^6)}

Question

Simplify the expression

4

Evaluate

\frac{( x \times 8 ) x ^{6} \times 4}{( x \times 8 ) x ^{6}}

Remove the parentheses

\frac{x \times 8 x ^{6} \times 4}{x \times 8 x ^{6}}

Multiply

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Evaluate

x \times 8 x^{6} \times 4

Multiply the terms with the same base by adding their exponents

x^{1 + 6} \times 8 \times 4

Add the numbers

x^{7} \times 8 \times 4

Multiply the terms

x^{7} \times 32

\frac{x ^{7} \times 32}{x \times 8 x ^{6}}

Multiply

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Evaluate

x \times 8 x^{6}

Multiply the terms with the same base by adding their exponents

x^{1 + 6} \times 8

Add the numbers

x^{7} \times 8

\frac{x ^{7} \times 32}{x ^{7} \times 8}

Reduce the fraction

\frac{32}{8}

Solution

4

Show Solution

Find the excluded values

x = 0

Evaluate

\frac{( x \times 8 ) ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )}

To find the excluded values,set the denominators equal to 0

(x \times 8) (x^{6}) = 0

Solution

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Evaluate

(x \times 8) x^{6} = 0

Remove the parentheses

x \times 8 x^{6} = 0

Multiply

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Evaluate

x \times 8 x^{6}

Multiply the terms with the same base by adding their exponents

x^{1 + 6} \times 8

Add the numbers

x^{7} \times 8

Use the commutative property to reorder the terms

8 x^{7}

8 x^{7} = 0

Rewrite the expression

x^{7} = 0

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

x = 0

x = 0

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Find the roots

x \in \emptyset

Evaluate

\frac{( x \times 8 ) ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )}

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

\frac{( x \times 8 ) ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )} = 0

Find the domain

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Evaluate

{x \times 8 x^{6} \neq = 0 (x \times 8) (x^{6}) \neq = 0

Calculate

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Evaluate

x \times 8 x^{6} \neq = 0

Multiply

8 x^{7} \neq = 0

Rewrite the expression

x^{7} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

{x \neq = 0 (x \times 8) (x^{6}) \neq = 0

Calculate

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Evaluate

(x \times 8) x^{6} \neq = 0

Remove the parentheses

x \times 8 x^{6} \neq = 0

Multiply

8 x^{7} \neq = 0

Rewrite the expression

x^{7} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

{x \neq = 0 x \neq = 0

Find the intersection

x \neq = 0

\frac{( x \times 8 ) ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )} = 0, x \neq = 0

Calculate

\frac{( x \times 8 ) ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )} = 0

Use the commutative property to reorder the terms

\frac{8 x ( x ^{6} ) \times 4}{( x \times 8 ) ( x ^{6} )} = 0

Calculate

\frac{8 x \times x ^{6} \times 4}{( x \times 8 ) ( x ^{6} )} = 0

Use the commutative property to reorder the terms

\frac{8 x \times x ^{6} \times 4}{8 x ( x ^{6} )} = 0

Calculate

\frac{8 x \times x ^{6} \times 4}{8 x \times x ^{6}} = 0

Multiply

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Multiply the terms

8 x \times x^{6} \times 4

Multiply the terms

32 x \times x^{6}

Multiply the terms with the same base by adding their exponents

32 x^{1 + 6}

Add the numbers

32 x^{7}

\frac{32 x ^{7}}{8 x \times x ^{6}} = 0

Multiply the terms

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Evaluate

x \times x^{6}

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

x^{1 + 6}

Add the numbers

x^{7}

\frac{32 x ^{7}}{8 x ^{7}} = 0

Divide the terms

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Evaluate

\frac{32 x ^{7}}{8 x ^{7}}

Reduce the fraction

\frac{32}{8}

Reduce the numbers

\frac{4}{1}

Calculate

4

4 = 0

Solution

x \in \emptyset

Show Solution