Simplify 9xy^2*9x^5y^2

$9 x y^{2} \cdot 9 x^{5} y^{2}$

Step 1

Multiply $x$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$9 (x^{5} x) y^{2} \cdot (9 y^{2})$

Multiply $x^{5}$ by $x$ .

Raise $x$ to the power of $1$ .

$9 (x^{5} x^{1}) y^{2} \cdot (9 y^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 x^{5 + 1} y^{2} \cdot (9 y^{2})$

Add $5$ and $1$ .

$9 x^{6} y^{2} \cdot (9 y^{2})$

Step 2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$9 x^{6} (y^{2} y^{2}) \cdot 9$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 x^{6} y^{2 + 2} \cdot 9$

Add $2$ and $2$ .

$9 x^{6} y^{4} \cdot 9$

Step 3

Multiply $9$ by $9$ .

$81 x^{6} y^{4}$