How do you simplify ${(\frac{8 x^{3}}{27 y^{6}})}^{\frac{1}{3}}$ $((8x^3 )/ (27y^6))^(1/3)$ ?

Question

How do you simplify ${(\frac{8 x^{3}}{27 y^{6}})}^{\frac{1}{3}}$ $((8x^3 )/ (27y^6))^(1/3)$ ?

1 Answer

Impact of this question

2194 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-01T08:24:21

$\frac{2 x}{3 y^{2}}$ $(2x)/(3y^2)$

Explanation:

${(\frac{8 x^{3}}{27 y^{6}})}^{\frac{1}{3}}$ $((8x^3)/(27y^6))^(1/3)$ is the same as ${(\frac{2^{3} x^{3}}{3^{3} y^{6}})}^{\frac{1}{3}}$ $((color(green)(2^3)x^3)/(color(green)(3^3)y^6))^(1/3)$

Distribute the external exponent $(\frac{1}{3})$ $(color(red)(1/3))$ into the exponents inside (for both numerator and the denominator)

${(\frac{2^{3} x^{3}}{3^{3} y^{6}})}^{\frac{1}{3}} = \frac{2^{3 \cdot \frac{1}{3}} x^{3 \cdot \frac{1}{3}}}{3^{3 \cdot \frac{1}{3}} y^{6 \cdot \frac{1}{3}}} = \frac{2 x}{3 y^{2}}$ $((color(green)(2^3)x^3)/(color(green)(3^3)y^6))^color(red)(1/3)=(color(green)(2^(3*color(red)(1/3)))x^(3*color(red)(1/3)))/(color(green)(3^(3*color(red)(1/3)))y^(6*color(red)(1/3)))=(color(green)2x)/(color(green)3y^2)$

Science

Math

Humanities

... and beyond

How do you simplify ${(\frac{8 x^{3}}{27 y^{6}})}^{\frac{1}{3}}$ $((8x^3 )/ (27y^6))^(1/3)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify ((8x^3 )/ (27y^6))^(1/3)(8x327y6)13 ((8x^3 )/ (27y^6))^(1/3)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify ${(\frac{8 x^{3}}{27 y^{6}})}^{\frac{1}{3}}$ $((8x^3 )/ (27y^6))^(1/3)$ ?