Question
8x^5y^7 divided by 4x^3y^4 simplify using algebra 1 exponential rules
Answers
GPT-4o mini
To simplify the expression \(\frac{8x^5y^7}{4x^3y^4}\) 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 \(y\):
\[
2x^2y^3
\]
Thus, the simplified form of \(\frac{8x^5y^7}{4x^3y^4}\) is:
\[
\boxed{2x^2y^3}
\]
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 \(y\):
\[
2x^2y^3
\]
Thus, the simplified form of \(\frac{8x^5y^7}{4x^3y^4}\) is:
\[
\boxed{2x^2y^3}
\]