Question

What is the product of (10x^4y^2)*(3xy^3)

Answer 1

Answer:
`30x^5y^5`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)`

`x^4x=\:x^(4+1)`

`=10y^2\cdot \:3x^(4+1)y^3`

`\mathrm{Add\:the\:numbers:}\:4+1=5`

`=10y^2\cdot \:3x^5y^3`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^(b+c)\\ y^2y^3=\:y^(2+3)\\ =10\cdot \:3x^5y^(2+3)\\ \mathrm{Add\:the\:numbers:}\:2+3=5\\ =10\cdot \:3x^5y^5\\ \mathrm{Multiply\:the\:numbers:}\:10\cdot \:3=30\\ =30x^5y^5\\`

Final Answer:
`30x^5y^5`