Solve (x^6)^(-1/4)

Question

Simplify the expression

\frac{x}{x ^{2}}

Evaluate

(x^{6})^{- \frac{1}{4}}

Multiply the exponents

x^{6 (- \frac{1}{4})}

Multiply the numbers

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Evaluate

6 (- \frac{1}{4})

Multiplying or dividing an odd number of negative terms equals a negative

- 6 \times \frac{1}{4}

Reduce the numbers

- 3 \times \frac{1}{2}

Multiply the numbers

- \frac{3}{2}

x^{- \frac{3}{2}}

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

\frac{1}{x ^{\frac{3}{2}}}

Transform the expression

More Steps

Evaluate

x^{\frac{3}{2}}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

x^{3}

Rewrite the exponent as a sum

x^{2 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

x^{2} \times x

The root of a product is equal to the product of the roots of each factor

x^{2} \times x

Reduce the index of the radical and exponent with 2

x x

\frac{1}{x x}

Multiply by the Conjugate

\frac{1 \times x}{x x \times x}

Calculate

\frac{1 \times x}{x \times x}

Any expression multiplied by 1 remains the same

\frac{x}{x \times x}

Solution

\frac{x}{x ^{2}}

Show Solution

x \in \emptyset

Evaluate

(x^{6})^{- \frac{1}{4}}

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

(x^{6})^{- \frac{1}{4}} = 0

Find the domain

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Evaluate

{x^{6} > 0 x^{6} \neq = 0

Calculate

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Evaluate

x^{6} > 0

Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when x^{6} = 0

x^{6} = 0

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

x = 0

Exclude the impossible values of x

x \neq = 0

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

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

{x \neq = 0 x \neq = 0

Find the intersection

x \neq = 0

(x^{6})^{- \frac{1}{4}} = 0, x \neq = 0

Calculate

(x^{6})^{- \frac{1}{4}} = 0

Evaluate the power

More Steps

Evaluate

(x^{6})^{- \frac{1}{4}}

Transform the expression

x^{6 (- \frac{1}{4})}

Multiply the numbers

More Steps

Evaluate

6 (- \frac{1}{4})

Multiplying or dividing an odd number of negative terms equals a negative

- 6 \times \frac{1}{4}

Reduce the numbers

- 3 \times \frac{1}{2}

Multiply the numbers

- \frac{3}{2}

x^{- \frac{3}{2}}

x^{- \frac{3}{2}} = 0

Rewrite the expression

\frac{1}{x ^{\frac{3}{2}}} = 0

Cross multiply

1 = x^{\frac{3}{2}} \times 0

Simplify the equation

1 = 0

Solution

x \in \emptyset

Show Solution