Simplify 16 root of xx^3x^4

$\sqrt[16]{x \cdot x^{3} \cdot x^{4}}$

Step 1

Multiply $x$ by $x^{3}$ by adding the exponents.

Multiply $x$ by $x^{3}$ .

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

$\sqrt[16]{x^{1} \cdot x^{3} x^{4}}$

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

$\sqrt[16]{x^{1 + 3} x^{4}}$

Add $1$ and $3$ .

$\sqrt[16]{x^{4} x^{4}}$

Step 2

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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

$\sqrt[16]{x^{4 + 4}}$

Add $4$ and $4$ .

$\sqrt[16]{x^{8}}$

Step 3

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$\sqrt[16]{{(x^{2})}^{4}}$

Step 4

Rewrite $\sqrt[16]{{(x^{2})}^{4}}$ as $\sqrt[4]{\sqrt[4]{{(x^{2})}^{4}}}$ .

$\sqrt[4]{\sqrt[4]{{(x^{2})}^{4}}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[4]{x^{2}}$

Step 6

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

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

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{x}$

Simplify 16 root of x*x^3*x^4