Simplify 4x^2 square root of 5x^4*3 square root of 5x^8

$4 x^{2} \sqrt{5 x^{4}} \cdot 3 \sqrt{5 x^{8}}$

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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

$4 x^{2} \sqrt{5 {(x^{2})}^{2}} \cdot (3 \sqrt{5 x^{8}})$

Reorder $5$ and ${(x^{2})}^{2}$ .

$4 x^{2} \sqrt{{(x^{2})}^{2} \cdot 5} \cdot (3 \sqrt{5 x^{8}})$

Pull terms out from under the radical.

$4 x^{2} (x^{2} \sqrt{5}) \cdot (3 \sqrt{5 x^{8}})$

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

Move $x^{2}$ .

$4 (x^{2} x^{2}) \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

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

$4 x^{2 + 2} \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

Add $2$ and $2$ .

$4 x^{4} \sqrt{5} \cdot (3 \sqrt{5 x^{8}})$

Rewrite $5 x^{8}$ as ${({(x^{2})}^{2})}^{2} \cdot 5$ .

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

$4 x^{4} \sqrt{5} \cdot (3 \sqrt{5 {(x^{4})}^{2}})$

Reorder $5$ and ${(x^{4})}^{2}$ .

$4 x^{4} \sqrt{5} \cdot (3 \sqrt{{(x^{4})}^{2} \cdot 5})$

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

$4 x^{4} \sqrt{5} \cdot (3 \sqrt{{({(x^{2})}^{2})}^{2} \cdot 5})$

Pull terms out from under the radical.

$4 x^{4} \sqrt{5} \cdot (3 ({(x^{2})}^{2} \sqrt{5}))$

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$4 x^{4} \sqrt{5} \cdot (3 (x^{2 \cdot 2} \sqrt{5}))$

Multiply $2$ by $2$ .

$4 x^{4} \sqrt{5} \cdot (3 (x^{4} \sqrt{5}))$

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

Move $x^{4}$ .

$4 (x^{4} x^{4}) \sqrt{5} \cdot (3 (\sqrt{5}))$

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

$4 x^{4 + 4} \sqrt{5} \cdot (3 (\sqrt{5}))$

Add $4$ and $4$ .

$4 x^{8} \sqrt{5} \cdot (3 (\sqrt{5}))$

Multiply $4 x^{8} \sqrt{5} (3 \sqrt{5})$ .

Multiply $3$ by $4$ .

$12 x^{8} \sqrt{5} \sqrt{5}$

Raise $\sqrt{5}$ to the power of $1$ .

$12 x^{8} ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$12 x^{8} ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$12 x^{8} {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$12 x^{8} {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$12 x^{8} {(5^{\frac{1}{2}})}^{2}$

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

$12 x^{8} \cdot 5^{\frac{1}{2} \cdot 2}$

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

$12 x^{8} \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12 x^{8} \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$12 x^{8} \cdot 5^{1}$

Evaluate the exponent.

$12 x^{8} \cdot 5$

Multiply $5$ by $12$ .

$60 x^{8}$

Simplify 4x^2 square root of 5x^4*3 square root of 5x^8

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