What is [(3x^2y^3)^2]^3 ?

The solution to [(3x^2y^3)^2]^3 is 729x^{12}y^{18}

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simplify [(3x^2y^3)^2]^3

simplify

[(3 x^{2} y^{3})^{2}]^{3}

729 x^{12} y^{18}

Solution steps

((3 x^{2} y^{3})^{2})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (3 x^{2} y^{3})^{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= (3 x^{2} y^{3})^{6}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 x^{2} y^{3})^{6} = 3^{6} (x^{2})^{6} (y^{3})^{6}

= 3^{6} (x^{2})^{6} (y^{3})^{6}

3^{6} = 729

= 729 (x^{2})^{6} (y^{3})^{6}

Simplify

(x^{2})^{6} : x^{12}

= 729 x^{12} (y^{3})^{6}

Simplify

(y^{3})^{6} : y^{18}

= 729 x^{12} y^{18}

(\frac{2 v q ^{6}}{q v ^{3}})^{- 2}

4 - 3 (1.9999)^{3}

(3 x - 12) (x + 4)

(2 + 3 i) + (4 - 2 i)

\frac{72}{25}