Solve (2/9)(x^3 2)^(3/2)

Question

Simplify the expression

\frac{4 2 x \times x ^{4}}{9}

Evaluate

\frac{2}{9} (x^{3} \times 2)^{\frac{3}{2}}

Use the commutative property to reorder the terms

\frac{2}{9} (2 x^{3})^{\frac{3}{2}}

Rewrite the expression

\frac{2}{9} \times 2^{\frac{3}{2}} x^{\frac{9}{2}}

Multiply the numbers

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Evaluate

\frac{2}{9} \times 2^{\frac{3}{2}}

Multiply the numbers

\frac{2 \times 2 ^{\frac{3}{2}}}{9}

Multiply the numbers

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Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Multiply the numbers

2^{\frac{5}{2}}

\frac{2 ^{\frac{5}{2}}}{9}

\frac{2 ^{\frac{5}{2}}}{9} x^{\frac{9}{2}}

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

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Evaluate

2^{\frac{5}{2}}

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

2^{5}

Rewrite the expression

2^{4} \times 2

Rewrite the expression

2^{4} \times 2

Rewrite the expression

2^{2} 2

Calculate

42

\frac{4 2}{9} x^{\frac{9}{2}}

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

\frac{4 2}{9} x^{9}

Simplify the radical expression

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Evaluate

x^{9}

Rewrite the exponent as a sum

x^{8 + 1}

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

x^{8} \times x

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

x^{8} \times x

Reduce the index of the radical and exponent with 2

x^{4} x

\frac{4 2}{9} x^{4} x

Calculate the product

\frac{4 2 x}{9} x^{4}

Solution

\frac{4 2 x \times x ^{4}}{9}

Show Solution

Find the roots

x = 0

Evaluate

(\frac{2}{9}) (x^{3} \times 2)^{\frac{3}{2}}

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

(\frac{2}{9}) (x^{3} \times 2)^{\frac{3}{2}} = 0

Find the domain

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Evaluate

x^{3} \times 2 \geq 0

Use the commutative property to reorder the terms

2 x^{3} \geq 0

Rewrite the expression

x^{3} \geq 0

The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0

x \geq 0

(\frac{2}{9}) (x^{3} \times 2)^{\frac{3}{2}} = 0, x \geq 0

Calculate

(\frac{2}{9}) (x^{3} \times 2)^{\frac{3}{2}} = 0

Use the commutative property to reorder the terms

(\frac{2}{9}) (2 x^{3})^{\frac{3}{2}} = 0

Remove the unnecessary parentheses

\frac{2}{9} (2 x^{3})^{\frac{3}{2}} = 0

Multiply the terms

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Evaluate

\frac{2}{9} (2 x^{3})^{\frac{3}{2}}

Rewrite the expression

\frac{2}{9} \times 22 \times x^{\frac{9}{2}}

Multiply the numbers

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Evaluate

\frac{2}{9} \times 22

Multiply the numbers

\frac{2 \times 2 2}{9}

Multiply the numbers

\frac{4 2}{9}

\frac{4 2}{9} x^{\frac{9}{2}}

\frac{4 2}{9} x^{\frac{9}{2}} = 0

Rewrite the expression

x^{\frac{9}{2}} = 0

The only way a root could be 0 is when the radicand equals 0

x = 0

Check if the solution is in the defined range

x = 0, x \geq 0

Solution

x = 0

Show Solution