a. $$ \left(2 x^{3} y\right)^{2}\left(3 x^{0} y^{4}\right)^{5} $$

Question

UpStudy AI · Accepted Answer

1. Primero, separamos la expresión en dos partes y aplicamos la propiedad de la potencia:

$$
   \left(2 x^{3} y\right)^{2} = 2^{2}\left(x^{3}\right)^{2}y^{2}
   $$

$$
   \left(3 x^{0} y^{4}\right)^{5} = 3^{5}\left(x^{0}\right)^{5}\left(y^{4}\right)^{5}
   $$

2. Se simplifican los exponentes en cada factor:

- Para la primera parte:

$$
     2^{2} = 4, \quad \left(x^{3}\right)^{2} = x^{3\times2} = x^{6}, \quad y^{2}= y^{2}
     $$

Entonces:

$$
     \left(2 x^{3} y\right)^{2} = 4x^{6}y^{2}
     $$

- Para la segunda parte:

$$
     3^{5} = 243, \quad \left(x^{0}\right)^{5} = x^{0\times5} = x^{0} = 1, \quad \left(y^{4}\right)^{5} = y^{4\times5} = y^{20}
     $$

Entonces:

$$
     \left(3 x^{0} y^{4}\right)^{5} = 243 \cdot 1 \cdot y^{20} = 243y^{20}
     $$

3. Finalmente, se multiplican ambas expresiones:

$$
   4x^{6}y^{2} \cdot 243y^{20} = (4 \cdot 243)x^{6}y^{2+20}
   $$

$$
   4 \cdot 243 = 972 \quad \text{y} \quad y^{2+20} = y^{22}
   $$

Entonces, la expresión final es:

$$
   972x^{6}y^{22}
   $$
La expresión simplificada es $$ 972x^{6}y^{22} $$.

a. \( \left(2 x^{3} y\right)^{2}\left(3 x^{0} y^{4}\right)^{5} \)