How do you simplify ${(z^{- 4} \cdot x^{\frac{3}{5}})}^{\frac{1}{3}}$ $(z ^ { - 4} \cdot x ^ { \frac { 3} { 5} } ) ^ { \frac { 1} { 3} }$ ?

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Answer 1 · 2017-05-06T08:13:22

$z^{- \frac{4}{3}} \cdot x^{\frac{1}{5}} = \frac{\sqrt[5]{x}}{z \sqrt[3]{z}}$ $z^(-4/3)*x^(1/5)=root(5)x/(zroot(3)(z))$

Since ${(a^{b})}^{c} = a^{b c}$ $(a^b)^c=a^(bc)$ , you would get:

${(z^{- 4} \cdot x^{\frac{3}{5}})}^{\frac{1}{3}} = z^{- \frac{4}{3}} \cdot x^{\frac{1}{5}}$ $(z^-4*x^(3/5))^(1/3)=z^(-4/3)*x^(1/5)$

and, since $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ $a^(m/n)=root(n)(a^m)$ , you could write the equivalent expression:

$\frac{\sqrt[5]{x}}{\sqrt[3]{z^{4}}} = \frac{\sqrt[5]{x}}{z \sqrt[3]{z}}$ $root(5)x/root(3)(z^4)=root(5)x/(zroot(3)(z))$

How do you simplify (z ^ { - 4} \cdot x ^ { \frac { 3} { 5} } ) ^ { \frac { 1} { 3} }(z−4⋅x35)13(z ^ { - 4} \cdot x ^ { \frac { 3} { 5} } ) ^ { \frac { 1} { 3} }?