So here are 4 rules when it comes to exponents:
- When you raise a power to a power, you really just multiply the exponents: [tex] (x^m)^n=x^{m*n} [/tex]
- When you multiply 2 exponents of the same base, you add the exponents together: [tex] x^m*x^n=x^{m+n} [/tex]
- When you divide 2 exponents of the same base, you subtract the exponents: [tex] \frac{x^m}{x^n}=x^{m-n} [/tex]
- To convert a negative exponent into a positive one, flip it to its reciprocal: [tex] x^{-m}=\frac{1}{x^m}\\ \frac{1}{x^{-m}}=\frac{x^{m}}{1}=x^m [/tex]
Part A:
[tex] \frac{2x^3y^3}{4y^2}=\frac{1}{2}x^{3-0}y^{3-2}=\frac{1}{2}x^3y [/tex]
Part B:
[tex] (\frac{x^{-8}}{y^{11}})^{-2}=\frac{x^{-8*-2}}{y^{11*-2}}=\frac{x^{16}}{y^{-22}}=\frac{x^{16}y^{22}}{1}=x^{16}y^{22} [/tex]
Part C:
[tex] \frac{(2x^3)(x^4)^2}{8x^{11}}=\frac{(2x^3)(x^{4*2})}{8x^{11}}=\frac{(2x^3)(x^8)}{8x^{11}}=\frac{2x^{3+8}}{8x^{11}}=\frac{2x^{11}}{8x^{11}}=\frac{1}{4}x^{11-11}=\frac{1}{4}x^0=\frac{1}{4} [/tex]
