Algebra Examples

$x \sqrt{54 x^{4} y^{6}}$

Step 1

Rewrite $54 x^{4} y^{6}$ as ${(3 x^{2} y^{3})}^{2} \cdot 6$ .

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Step 1.1

Factor $9$ out of $54$ .

$x \sqrt{9 (6) x^{4} y^{6}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$x \sqrt{3^{2} \cdot 6 x^{4} y^{6}}$

Step 1.3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$x \sqrt{3^{2} \cdot 6 {(x^{2})}^{2} y^{6}}$

Step 1.4

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$x \sqrt{3^{2} \cdot 6 {(x^{2})}^{2} {(y^{3})}^{2}}$

Step 1.5

Move $6$ .

$x \sqrt{3^{2} {(x^{2})}^{2} {(y^{3})}^{2} \cdot 6}$

Step 1.6

Rewrite $3^{2} {(x^{2})}^{2} {(y^{3})}^{2}$ as ${(3 x^{2} y^{3})}^{2}$ .

$x \sqrt{{(3 x^{2} y^{3})}^{2} \cdot 6}$

Step 2

Pull terms out from under the radical.

$x (| 3 x^{2} y^{3} | \sqrt{6})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{6} x | 3 x^{2} y^{3} |$

Step 4

Remove non-negative terms from the absolute value.

$\sqrt{6} x (3 x^{2} | y^{3} |)$

Step 5

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 5.1

Move $x^{2}$ .

$\sqrt{6} (x^{2} x) (3 | y^{3} |)$

Step 5.2

Multiply $x^{2}$ by $x$ .

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Step 5.2.1

Raise $x$ to the power of $1$ .

$\sqrt{6} (x^{2} x^{1}) (3 | y^{3} |)$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{6} x^{2 + 1} (3 | y^{3} |)$

Step 5.3

Add $2$ and $1$ .

$\sqrt{6} x^{3} (3 | y^{3} |)$

Step 6

Move $3$ to the left of $\sqrt{6} x^{3}$ .

$3 \sqrt{6} x^{3} | y^{3} |$