Simplify square root of 64x^9* fourth root of 256x^10

$\sqrt{64 x^{9}} \cdot \sqrt[4]{256 x^{10}}$

Rewrite $64 x^{9}$ as ${(8 x^{4})}^{2} x$ .

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} x^{9}} \cdot \sqrt[4]{256 x^{10}}$

Factor out $x^{8}$ .

$\sqrt{8^{2} (x^{8} x)} \cdot \sqrt[4]{256 x^{10}}$

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

$\sqrt{8^{2} ({(x^{4})}^{2} x)} \cdot \sqrt[4]{256 x^{10}}$

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

$\sqrt{{(8 x^{4})}^{2} x} \cdot \sqrt[4]{256 x^{10}}$

Pull terms out from under the radical.

$8 x^{4} \sqrt{x} \cdot \sqrt[4]{256 x^{10}}$

Rewrite $256 x^{10}$ as ${(4 x^{2})}^{4} x^{2}$ .

Rewrite $256$ as $4^{4}$ .

$8 x^{4} \sqrt{x} \cdot \sqrt[4]{4^{4} x^{10}}$

Factor out $x^{8}$ .

$8 x^{4} \sqrt{x} \cdot \sqrt[4]{4^{4} (x^{8} x^{2})}$

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

$8 x^{4} \sqrt{x} \cdot \sqrt[4]{4^{4} ({(x^{2})}^{4} x^{2})}$

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

$8 x^{4} \sqrt{x} \cdot \sqrt[4]{{(4 x^{2})}^{4} x^{2}}$

Pull terms out from under the radical.

$8 x^{4} \sqrt{x} \cdot (4 x^{2} \sqrt[4]{x^{2}})$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$8 (x^{2} x^{4}) \sqrt{x} \cdot (4 \sqrt[4]{x^{2}})$

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

$8 x^{2 + 4} \sqrt{x} \cdot (4 \sqrt[4]{x^{2}})$

Add $2$ and $4$ .

$8 x^{6} \sqrt{x} \cdot (4 \sqrt[4]{x^{2}})$

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

$8 x^{6} \sqrt{x} \cdot (4 \sqrt{\sqrt{x^{2}}})$

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

$8 x^{6} \sqrt{x} \cdot (4 \sqrt{x})$

Multiply $8 x^{6} \sqrt{x} (4 \sqrt{x})$ .

Multiply $4$ by $8$ .

$32 x^{6} \sqrt{x} \sqrt{x}$

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

$32 x^{6} ({\sqrt{x}}^{1} \sqrt{x})$

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

$32 x^{6} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$32 x^{6} {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$32 x^{6} {\sqrt{x}}^{2}$

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

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

$32 x^{6} {(x^{\frac{1}{2}})}^{2}$

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

$32 x^{6} x^{\frac{1}{2} \cdot 2}$

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

$32 x^{6} x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$32 x^{6} x^{\frac{2}{2}}$

Rewrite the expression.

$32 x^{6} x^{1}$

Simplify.

$32 x^{6} x$

Multiply $x^{6}$ by $x$ by adding the exponents.

Move $x$ .

$32 (x \cdot x^{6})$

Multiply $x$ by $x^{6}$ .

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

$32 (x^{1} x^{6})$

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

$32 x^{1 + 6}$

Add $1$ and $6$ .

$32 x^{7}$

Simplify square root of 64x^9* fourth root of 256x^10

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