Question

Como resuelvo este binomio
(xy²)³ *(-5x³y²)²

Answer 1

Respuesta: $25x^9y^{10}$

Explicación paso a paso:

$\left(xy^2\right)^3\left(-5x^3y^2\right)^2\\\\\left(xy^2\right)^3\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a\cdot \:b\right)^n=a^nb^n\\\\=x^3\left(y^2\right)^3\\\\\left(y^2\right)^3\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a^b\right)^c=a^{bc}\\\\=y^{2\cdot \:3}=y^6\\\\=x^3y^6\left(-5x^3y^2\right)^2$

$\left(-5x^3y^2\right)^2\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(-a\right)^n=a^n,\:\mathrm{si\:}n\mathrm{\:es\:par}\\\\=\left(5x^3y^2\right)^2\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a\cdot \:b\right)^n=a^nb^n\\\\=5^2\left(x^3\right)^2\left(y^2\right)^2\\\\\left(x^3\right)^2=x^{3\cdot \:2}=x^6\\\\=5^2x^6\left(y^2\right)^2\\\\\left(y^2\right)^2=y^{2\cdot \:2}=y^4\\\\=5^2x^6y^4$

$5^2x^6x^3y^6y^4\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\\=y^6\cdot \:5^2x^{3+6}y^4=y^6\cdot \:5^2x^9y^4\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\\=5^2x^9y^{6+4}\\\\=25x^9y^{10}$