Question

Choose the correct simplification of the expression (4x3y2z4)(2x3y4z3)

Answer 1

`=8x^6y^6z^7`

Explanation:

`(4x^3*y^2*z^4)(2x^3*y^4*z^3)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\\:a^c=a^(b+c)\\=4y^2z^4\cdot \:2x^(3+3)y^4z^3\\\mathrm{Add\:the\:numbers:}\:3+3=6\\=4y^2z^4\cdot \:2x^6y^4z^3\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\y^2y^4=\:y^(2+4)\\=4z^4\cdot \:2x^6y^(2+4)z^3`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\z^4z^3=\:z^(4+3)\\=4\cdot \:2x^6y^6z^(4+3)\\\mathrm{Add\:the\:numbers:}\:4+3=7\\=4\cdot \:2x^6y^6z^7\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=8x^6y^6z^7`