8x^5y^7 divided by 4x^3y^4 simplify using algebra 1 exponential rules

Answer 1

To simplify the expression $\frac{8x^5{y}^7}{4x^3{y}^4}$ using algebraic rules for exponents, follow these steps:

1. Simplify the coefficients: Divide the coefficients (numerical parts) first: $$\frac{8}{4}=2$$

2. Apply the quotient rule for exponents for $x$: The quotient rule states that $\frac{a^m}{a^n}=a^{m-n}$. Here, you will subtract the exponents of $x$: $$\frac{x^5}{x^3}=x^{5-3}=x^2$$

3. Apply the quotient rule for exponents for $y$: Similarly, for $y$: $$\frac{y^7}{y^4}=y^{7-4}=y^3$$

4. Combine all parts together: Now combine the simplified coefficient and the terms with $x$ and $y$: $$2x^2{y}^3$$

Thus, the simplified form of $\frac{8x^5{y}^7}{4x^3{y}^4}$ is: $$\boxed{{\displaystyle 2x^2{y}^3}}$$