Solve 4x root(2)(2x ) 4x root(2)(x)

Question

Simplify the expression

162 \times x^{3}

Evaluate

4 x 2 x \times 4 x x

Multiply the terms

16 x 2 x \times x x

Multiply the terms

16 x^{2} 2 x \times x

Multiply the terms

More Steps

Evaluate

2 x \times x

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

2 x \times x

Calculate the product

2 x^{2}

Reorder the terms

x^{2} \times 2

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

x^{2} \times 2

Reduce the index of the radical and exponent with 2

2 \times x

16 x^{2} 2 \times x

Multiply the numbers

162 \times x^{2} \times x

Solution

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

162 \times x^{3}

Show Solution

Find the roots

x = 0

Evaluate

4 x 2 x \times 4 x x

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

4 x 2 x \times 4 x x = 0

Find the domain

More Steps

Evaluate

{2 x \geq 0 x \geq 0

Calculate

{x \geq 0 x \geq 0

Find the intersection

x \geq 0

4 x 2 x \times 4 x x = 0, x \geq 0

Calculate

4 x 2 x \times 4 x x = 0

Multiply

More Steps

Multiply the terms

4 x 2 x \times 4 x x

Multiply the terms

16 x 2 x \times x x

Multiply the terms

16 x^{2} 2 x \times x

Multiply the terms

More Steps

Evaluate

2 x \times x

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

2 x \times x

Calculate the product

2 x^{2}

Reorder the terms

x^{2} \times 2

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

x^{2} \times 2

Reduce the index of the radical and exponent with 2

2 \times x

16 x^{2} 2 \times x

Multiply the numbers

162 \times x^{2} \times x

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

162 \times x^{3}

162 \times x^{3} = 0

Rewrite the expression

x^{3} = 0

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

x = 0

Check if the solution is in the defined range

x = 0, x \geq 0

Solution

x = 0

Show Solution