Solve sqrt{8x^9}\cdot \sqrt{18x^5}

Question

Simplify the expression

12 x^{7}

Evaluate

8 x^{9} \times 18 x^{5}

Simplify the root

More Steps

Evaluate

8 x^{9}

Rewrite the exponent as a sum

2^{2 + 1} x^{8 + 1}

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

2^{2} \times 2 x^{8} \times x

Reorder the terms

2^{2} x^{8} \times 2 x

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

2^{2} x^{8} \times 2 x

Reduce the index of the radical and exponent with 2

2 x^{4} 2 x

2 x^{4} 2 x \times 18 x^{5}

Simplify the root

More Steps

Evaluate

18 x^{5}

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2 x^{5}

Write the number in exponential form with the base of 3

3^{2} \times 2 x^{5}

Rewrite the exponent as a sum

3^{2} \times 2 x^{4 + 1}

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

3^{2} \times 2 x^{4} \times x

Reorder the terms

3^{2} x^{4} \times 2 x

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

3^{2} x^{4} \times 2 x

Reduce the index of the radical and exponent with 2

3 x^{2} 2 x

2 x^{4} 2 x \times 3 x^{2} 2 x

When a square root of an expression is multiplied by itself,the result is that expression

2 x^{4} \times 3 x^{2} \times 2 x

Multiply the terms

12 x^{4} \times x^{2} \times x

Calculate

More Steps

Multiply the terms

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

Calculate

x^{4 + 2}

Calculate

x^{6}

12 x^{6} \times x

Solution

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Multiply the terms

x^{6} \times x

Calculate

x^{6 + 1}

Calculate

x^{7}

12 x^{7}

Show Solution

Find the roots

x = 0

Evaluate

8 x^{9} \times 18 x^{5}

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

8 x^{9} \times 18 x^{5} = 0

Find the domain

More Steps

Evaluate

{8 x^{9} \geq 0 18 x^{5} \geq 0

Calculate

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Evaluate

8 x^{9} \geq 0

Rewrite the expression

x^{9} \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

{x \geq 0 18 x^{5} \geq 0

Calculate

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Evaluate

18 x^{5} \geq 0

Rewrite the expression

x^{5} \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

{x \geq 0 x \geq 0

Find the intersection

x \geq 0

8 x^{9} \times 18 x^{5} = 0, x \geq 0

Calculate

8 x^{9} \times 18 x^{5} = 0

Simplify the root

More Steps

Evaluate

8 x^{9}

Rewrite the exponent as a sum

2^{2 + 1} x^{8 + 1}

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

2^{2} \times 2 x^{8} \times x

Reorder the terms

2^{2} x^{8} \times 2 x

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

2^{2} x^{8} \times 2 x

Reduce the index of the radical and exponent with 2

2 x^{4} 2 x

2 x^{4} 2 x \times 18 x^{5} = 0

Simplify the root

More Steps

Evaluate

18 x^{5}

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2 x^{5}

Write the number in exponential form with the base of 3

3^{2} \times 2 x^{5}

Rewrite the exponent as a sum

3^{2} \times 2 x^{4 + 1}

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

3^{2} \times 2 x^{4} \times x

Reorder the terms

3^{2} x^{4} \times 2 x

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

3^{2} x^{4} \times 2 x

Reduce the index of the radical and exponent with 2

3 x^{2} 2 x

2 x^{4} 2 x \times 3 x^{2} 2 x = 0

Multiply the terms

More Steps

Evaluate

2 x^{4} 2 x \times 3 x^{2} 2 x

When a square root of an expression is multiplied by itself,the result is that expression

2 x^{4} \times 3 x^{2} \times 2 x

Multiply the terms

12 x^{4} \times x^{2} \times x

Calculate

More Steps

Multiply the terms

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

Calculate

x^{4 + 2}

Calculate

x^{6}

12 x^{6} \times x

Calculate

More Steps

Multiply the terms

x^{6} \times x

Calculate

x^{6 + 1}

Calculate

x^{7}

12 x^{7}

12 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

Check if the solution is in the defined range

x = 0, x \geq 0

Solution

x = 0

Show Solution