square 5y^2cdot 7y^4 x^3y^5cdot x^8y^10

To solve the given expressions, we need to multiply the coefficients and add the exponents of the variables.<br /><br />1. For the expression $5y^{2}\cdot 7y^{4}$:<br /> - Multiply the coefficients: $5 \cdot 7 = 35$<br /> - Add the exponents of $y$: $2 + 4 = 6$<br /> - Therefore, the simplified expression is $35y^{6}$.<br /><br />2. For the expression $x^{3}y^{5}\cdot x^{8}y^{10}$:<br /> - Multiply the coefficients: $1 \cdot 1 = 1$<br /> - Add the exponents of $x$: $3 + 8 = 11$<br /> - Add the exponents of $y$: $5 + 10 = 15$<br /> - Therefore, the simplified expression is $x^{11}y^{15}$.<br /><br />So, the final answers are:<br />1. $35y^{6}$<br />2. $x^{11}y^{15}$