Question

Please help !!! I can’t solve this The teacher doesn’t teach well

Answer 1

So here are 4 rules when it comes to exponents:

1. When you raise a power to a power, you really just multiply the exponents: $(x^m)^n=x^{m*n}$
2. When you multiply 2 exponents of the same base, you add the exponents together: $x^m*x^n=x^{m+n}$
3. When you divide 2 exponents of the same base, you subtract the exponents: $\frac{x^m}{x^n}=x^{m-n}$
4. To convert a negative exponent into a positive one, flip it to its reciprocal: $x^{-m}=\frac{1}{x^m}\\ \frac{1}{x^{-m}}=\frac{x^{m}}{1}=x^m$

Part A:

$\frac{2x^3y^3}{4y^2}=\frac{1}{2}x^{3-0}y^{3-2}=\frac{1}{2}x^3y$

Part B:

$(\frac{x^{-8}}{y^{11}})^{-2}=\frac{x^{-8*-2}}{y^{11*-2}}=\frac{x^{16}}{y^{-22}}=\frac{x^{16}y^{22}}{1}=x^{16}y^{22}$

Part C:

$\frac{(2x^3)(x^4)^2}{8x^{11}}=\frac{(2x^3)(x^{4*2})}{8x^{11}}=\frac{(2x^3)(x^8)}{8x^{11}}=\frac{2x^{3+8}}{8x^{11}}=\frac{2x^{11}}{8x^{11}}=\frac{1}{4}x^{11-11}=\frac{1}{4}x^0=\frac{1}{4}$