To simplify the expression
[tex]\[
\frac{4 y^2 \cdot 5 y^7}{15 y^6}
\][/tex]
step-by-step, follow these steps:
1. Combine the terms in the numerator:
First, multiply the coefficients and the powers of [tex]\( y \)[/tex] in the numerator:
[tex]\[
4 y^2 \cdot 5 y^7 = (4 \cdot 5) \cdot (y^2 \cdot y^7)
\][/tex]
[tex]\[
4 \cdot 5 = 20
\][/tex]
[tex]\[
y^2 \cdot y^7 = y^{2+7} = y^9
\][/tex]
So, the numerator becomes:
[tex]\[
20 y^9
\][/tex]
2. Write the resulting expression:
[tex]\[
\frac{20 y^9}{15 y^6}
\][/tex]
3. Simplify the coefficients:
Divide the coefficients 20 and 15:
[tex]\[
\frac{20}{15} = \frac{20 \div 5}{15 \div 5} = \frac{4}{3}
\][/tex]
4. Simplify the powers of [tex]\( y \)[/tex]:
Subtract the exponents of [tex]\( y \)[/tex] in the numerator and the denominator:
[tex]\[
y^9 \div y^6 = y^{9-6} = y^3
\][/tex]
5. Combine the simplified coefficient with the simplified power of [tex]\( y \)[/tex]:
[tex]\[
\frac{4}{3} \cdot y^3 = \frac{4 y^3}{3}
\][/tex]
Thus, the simplified expression is:
[tex]\[
\frac{4 y^3}{3}
\][/tex]
So,
[tex]\[
\frac{4 y^2 \cdot 5 y^7}{15 y^6} = \frac{4 y^3}{3}
\][/tex]
