Algebra Examples

$\sqrt[4]{25 x^{2}} \cdot {(25 x^{2})}^{\frac{1}{4}}$

Step 1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt[4]{{(5 x)}^{2}} \cdot {(25 x^{2})}^{\frac{1}{4}}$

Step 2

Rewrite $\sqrt[4]{{(5 x)}^{2}}$ as $\sqrt{\sqrt{{(5 x)}^{2}}}$ .

$\sqrt{\sqrt{{(5 x)}^{2}}} \cdot {(25 x^{2})}^{\frac{1}{4}}$

Step 3

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

$\sqrt{5 x} \cdot {(25 x^{2})}^{\frac{1}{4}}$

Step 4

Apply the product rule to $25 x^{2}$ .

$\sqrt{5 x} \cdot (25^{\frac{1}{4}} {(x^{2})}^{\frac{1}{4}})$

Step 5

Rewrite using the commutative property of multiplication.

$25^{\frac{1}{4}} \sqrt{5 x} {(x^{2})}^{\frac{1}{4}}$

Step 6

Multiply the exponents in ${(x^{2})}^{\frac{1}{4}}$ .

Tap for more steps...

Step 6.1

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

$25^{\frac{1}{4}} \sqrt{5 x} x^{2 (\frac{1}{4})}$

Step 6.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1

Factor $2$ out of $4$ .

$25^{\frac{1}{4}} \sqrt{5 x} x^{2 \frac{1}{2 (2)}}$

Step 6.2.2

Cancel the common factor.

$25^{\frac{1}{4}} \sqrt{5 x} x^{2 \frac{1}{2 \cdot 2}}$

Step 6.2.3

Rewrite the expression.

$25^{\frac{1}{4}} \sqrt{5 x} x^{\frac{1}{2}}$