What is {e^{12*ln(x)+15*ln(y)}}^{1/3} ?

The solution to {e^{12*ln(x)+15*ln(y)}}^{1/3} is x^4y^5

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simplify {e^{12ln(x)+15ln(y)}}^{1/3}

simplify

{e^{12 \cdot l n (x) + 15 \cdot l n (y)}}^{\frac{1}{3}}

x^{4} y^{5}

Solution steps

{e^{12 l n (x) + 15 l n (y)}}^{\frac{1}{3}}

Apply exponent rule:

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

= e^{(12 l n (x) + 15 l n (y)) \frac{1}{3}}

Simplify

(12 ln (x) + 15 ln (y)) \frac{1}{3} : ln (x^{4} y^{5})

= e^{l n (x^{4} y^{5})}

Apply log rule:

a^{l o g_{a} (b)} = b

= x^{4} y^{5}

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

2 π

27

(3 m^{2} n^{2}) (- 2 m^{2} + n^{3})

- 2 g h (g^{3} h^{5})

What is {e^{12*ln(x)+15*ln(y)}}^{1/3} ?
The solution to {e^{12*ln(x)+15*ln(y)}}^{1/3} is x^4y^5