Question

simplify. express your answer using positive exponents. 9ycdot3y^{83}

Explanation:

Step1: Rewrite coefficients

Rewrite 9 as $3^2$. So the expression $9y\cdot3y$ becomes $3^2y\cdot3y$.

Step2: Multiply coefficients and variables

Use the rule of exponents $a^m\cdot a^n=a^{m + n}$ for the coefficients (where $a = 3$, $m=2$, $n = 1$) and multiply the $y$ - terms. The coefficient part is $3^2\times3=3^{2 + 1}=3^3$, and the variable part is $y\times y=y^{1+1}=y^2$. Then $3^2y\cdot3y=3^3y^2$.

Step3: Calculate the coefficient value

$3^3=3\times3\times3 = 27$. So the simplified expression is $27y^2$.

Answer:

$27y^2$