Question

Polynomials help please

Answer 1

This one can be tricky, just be sure to only work with like terms. So keep your regular numbers with your regular numbers (for example, 3 in this problem), keep your x's with your x's and your y's with your y's.

We need to make sure that we know a few rules. If you're multiplying the bases, then you add the exponents. For example: $a^{x} *a^{y} = a^{x + y}$

Dividing the bases means you subtract the exponents: $a^{x} / a^{y} = a^{x - y}$

And if you raise something with an exponent to another power, you multiply the exponents: $a^{x^{y} } or (a^{x})^{y} = a^{x*y}$

Applying these concepts, keep everything together, you should be able to group things as such:

$\frac{(3*5)(x^{-2}*x)(y^{-8}*y^{3})}{(x^{-3})^{4}y^{-2}}$

And simplify:

$\frac{(15)(x^{-1})(y^{-5})}{(x^{-12})y^{-2}}$

And further:

${(15)(x^{11})(y^{-3})}$

So finally:

$15x^{11}y^{-3}$ is our final answer.