What is (3y^{2/3})^3(2y^2)^2 ?

The solution to (3y^{2/3})^3(2y^2)^2 is 108y^6

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simplify (3y^{2/3})^3(2y^2)^2

simplify

(3 y^{\frac{2}{3}})^{3} (2 y^{2})^{2}

108 y^{6}

Solution steps

(3 y^{\frac{2}{3}})^{3} (2 y^{2})^{2}

Simplify

(3 y^{\frac{2}{3}})^{3} : 27 y^{2}

= 27 y^{2} (2 y^{2})^{2}

Simplify

(2 y^{2})^{2} : 4 y^{4}

= 27 y^{2} \cdot 4 y^{4}

Multiply the numbers:

27 \cdot 4 = 108

= 108 y^{2} y^{4}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y^{2} y^{4} = y^{2 + 4}

= 108 y^{2 + 4}

Add the numbers:

2 + 4 = 6

= 108 y^{6}

40 x^{2} - 48

1 \times 4

n \cdot n

(- 3 x y^{5})^{4}

lo g_{5} (125) - lo g_{5} (5)