Simplify ((25x^4)^(1/2))/(15x^2)

$\frac{{(25 x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

Simplify the numerator.

Apply the product rule to $25 x^{4}$ .

$\frac{25^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

Rewrite $25$ as $5^{2}$ .

$\frac{{(5^{2})}^{\frac{1}{2}} {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

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

$\frac{5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5^{2 (\frac{1}{2})} {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

Rewrite the expression.

$\frac{5^{1} {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

Evaluate the exponent.

$\frac{5 {(x^{4})}^{\frac{1}{2}}}{15 x^{2}}$

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

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

$\frac{5 x^{4 (\frac{1}{2})}}{15 x^{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{5 x^{2 (2) \frac{1}{2}}}{15 x^{2}}$

Cancel the common factor.

$\frac{5 x^{2 \cdot 2 \frac{1}{2}}}{15 x^{2}}$

Rewrite the expression.

$\frac{5 x^{2}}{15 x^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 x^{2}$ .

$\frac{5 (x^{2})}{15 x^{2}}$

Cancel the common factors.

Factor $5$ out of $15 x^{2}$ .

$\frac{5 (x^{2})}{5 (3 x^{2})}$

Cancel the common factor.

$\frac{5 x^{2}}{5 (3 x^{2})}$

Rewrite the expression.

$\frac{x^{2}}{3 x^{2}}$

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2}}{3 x^{2}}$

Rewrite the expression.

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$

Simplify ((25x^4)^(1/2))/(15x^2)

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