Simplify 64(x^4y^3)^(5/6)

$64 {(x^{4} y^{3})}^{\frac{5}{6}}$

Apply the product rule to $x^{4} y^{3}$ .

$64 ({(x^{4})}^{\frac{5}{6}} {(y^{3})}^{\frac{5}{6}})$

Multiply the exponents in ${(x^{4})}^{\frac{5}{6}}$ .

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

$64 (x^{4 (\frac{5}{6})} {(y^{3})}^{\frac{5}{6}})$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$64 (x^{2 (2) \frac{5}{6}} {(y^{3})}^{\frac{5}{6}})$

Factor $2$ out of $6$ .

$64 (x^{2 \cdot 2 \frac{5}{2 \cdot 3}} {(y^{3})}^{\frac{5}{6}})$

Cancel the common factor.

$64 (x^{2 \cdot 2 \frac{5}{2 \cdot 3}} {(y^{3})}^{\frac{5}{6}})$

Rewrite the expression.

$64 (x^{2 (\frac{5}{3})} {(y^{3})}^{\frac{5}{6}})$

Combine $2$ and $\frac{5}{3}$ .

$64 (x^{\frac{2 \cdot 5}{3}} {(y^{3})}^{\frac{5}{6}})$

Multiply $2$ by $5$ .

$64 (x^{\frac{10}{3}} {(y^{3})}^{\frac{5}{6}})$

Multiply the exponents in ${(y^{3})}^{\frac{5}{6}}$ .

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

$64 (x^{\frac{10}{3}} y^{3 (\frac{5}{6})})$

Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$64 (x^{\frac{10}{3}} y^{3 \frac{5}{3 (2)}})$

Cancel the common factor.

$64 (x^{\frac{10}{3}} y^{3 \frac{5}{3 \cdot 2}})$

Rewrite the expression.

$64 (x^{\frac{10}{3}} y^{\frac{5}{2}})$

$64 x^{\frac{10}{3}} y^{\frac{5}{2}}$

Simplify 64(x^4y^3)^(5/6)

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