Simplify square root of x^17* square root of x^11

$\sqrt{x^{17}} \cdot \sqrt{x^{11}}$

Step 1

Rewrite $x^{17}$ as ${(x^{8})}^{2} x$ .

Factor out $x^{16}$ .

$\sqrt{x^{16} x} \cdot \sqrt{x^{11}}$

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$\sqrt{{(x^{8})}^{2} x} \cdot \sqrt{x^{11}}$

Step 2

Pull terms out from under the radical.

$x^{8} \sqrt{x} \cdot \sqrt{x^{11}}$

Step 3

Rewrite $x^{11}$ as ${(x^{5})}^{2} x$ .

Factor out $x^{10}$ .

$x^{8} \sqrt{x} \cdot \sqrt{x^{10} x}$

Rewrite $x^{10}$ as ${(x^{5})}^{2}$ .

$x^{8} \sqrt{x} \cdot \sqrt{{(x^{5})}^{2} x}$

Step 4

Pull terms out from under the radical.

$x^{8} \sqrt{x} \cdot (x^{5} \sqrt{x})$

Step 5

Multiply $x^{8}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$x^{5} x^{8} \sqrt{x} \cdot \sqrt{x}$

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

$x^{5 + 8} \sqrt{x} \cdot \sqrt{x}$

Add $5$ and $8$ .

$x^{13} \sqrt{x} \cdot \sqrt{x}$

Step 6

Multiply $x^{13} \sqrt{x} \sqrt{x}$ .

Raise $\sqrt{x}$ to the power of $1$ .

$x^{13} ({\sqrt{x}}^{1} \sqrt{x})$

Raise $\sqrt{x}$ to the power of $1$ .

$x^{13} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$x^{13} {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$x^{13} {\sqrt{x}}^{2}$

Step 7

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$x^{13} {(x^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{13} x^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x^{13} x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{13} x^{\frac{2}{2}}$

Rewrite the expression.

$x^{13} x^{1}$

Simplify.

$x^{13} x$

Step 8

Multiply $x^{13}$ by $x$ by adding the exponents.

Multiply $x^{13}$ by $x$ .

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

$x^{13} x^{1}$

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

$x^{13 + 1}$

Add $13$ and $1$ .

$x^{14}$

Simplify square root of x^17* square root of x^11

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