Sure! Let's simplify the given expression step-by-step:
[tex]\[
\frac{5 x^6 y^7}{10 x^2 y^4}
\][/tex]
1. Separate the coefficients from the variables:
The expression can be broken down into three parts: the numerical coefficient, the powers of [tex]\(x\)[/tex], and the powers of [tex]\(y\)[/tex].
[tex]\[
\frac{5}{10} \cdot \frac{x^6}{x^2} \cdot \frac{y^7}{y^4}
\][/tex]
2. Simplify the coefficients:
Simplify the fraction [tex]\(\frac{5}{10}\)[/tex]:
[tex]\[
\frac{5}{10} = 0.5
\][/tex]
3. Simplify the powers of [tex]\(x\)[/tex]:
Apply the rule of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{x^6}{x^2} = x^{6-2} = x^4
\][/tex]
4. Simplify the powers of [tex]\(y\)[/tex]:
Similarly, apply the exponent rule:
[tex]\[
\frac{y^7}{y^4} = y^{7-4} = y^3
\][/tex]
5. Combine the simplified parts:
Putting it all together, we get:
[tex]\[
0.5 \cdot x^4 \cdot y^3 = 0.5 x^4 y^3
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\frac{5 x^6 y^7}{10 x^2 y^4} = 0.5 x^4 y^3
\][/tex]
