Simplify square root of 49x* fourth root of 16x^2

$\sqrt{49 x} \cdot \sqrt[4]{16 x^{2}}$

Step 1

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} x} \cdot \sqrt[4]{16 x^{2}}$

Step 2

Pull terms out from under the radical.

$7 \sqrt{x} \cdot \sqrt[4]{16 x^{2}}$

Step 3

Rewrite $16$ as $2^{4}$ .

$7 \sqrt{x} \cdot \sqrt[4]{2^{4} x^{2}}$

Step 4

Pull terms out from under the radical.

$7 \sqrt{x} \cdot (2 \sqrt[4]{x^{2}})$

Step 5

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

$7 \sqrt{x} \cdot (2 \sqrt{\sqrt{x^{2}}})$

Step 6

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

$7 \sqrt{x} \cdot (2 \sqrt{x})$

Step 7

Multiply $7 \sqrt{x} (2 \sqrt{x})$ .

Multiply $2$ by $7$ .

$14 \sqrt{x} \sqrt{x}$

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

$14 ({\sqrt{x}}^{1} \sqrt{x})$

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

$14 ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$14 {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$14 {\sqrt{x}}^{2}$

Step 8

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

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

$14 {(x^{\frac{1}{2}})}^{2}$

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

$14 x^{\frac{1}{2} \cdot 2}$

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

$14 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$14 x^{\frac{2}{2}}$

Rewrite the expression.

$14 x^{1}$

Simplify.

$14 x$

Simplify square root of 49x* fourth root of 16x^2

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