Simplify (25x^4)^(3/2)

${(25 x^{4})}^{\frac{3}{2}}$

Simplify the expression.

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

$25^{\frac{3}{2}} {(x^{4})}^{\frac{3}{2}}$

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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Raise $5$ to the power of $3$ .

$125 {(x^{4})}^{\frac{3}{2}}$

Multiply the exponents in ${(x^{4})}^{\frac{3}{2}}$ .

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

$125 x^{4 (\frac{3}{2})}$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$125 x^{2 (2) \frac{3}{2}}$

Cancel the common factor.

$125 x^{2 \cdot 2 \frac{3}{2}}$

Rewrite the expression.

$125 x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$125 x^{6}$

Simplify (25x^4)^(3/2)

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