Simplify a^2b^3c^5*ab^7c^2

$a^{2} b^{3} c^{5} \cdot a b^{7} c^{2}$

Step 1

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

Move $a$ .

$a \cdot a^{2} b^{3} c^{5} \cdot (b^{7} c^{2})$

Multiply $a$ by $a^{2}$ .

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

$a^{1} a^{2} b^{3} c^{5} \cdot (b^{7} c^{2})$

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

$a^{1 + 2} b^{3} c^{5} \cdot (b^{7} c^{2})$

Add $1$ and $2$ .

$a^{3} b^{3} c^{5} \cdot (b^{7} c^{2})$

Step 2

Multiply $b^{3}$ by $b^{7}$ by adding the exponents.

Move $b^{7}$ .

$a^{3} (b^{7} b^{3}) c^{5} \cdot c^{2}$

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

$a^{3} b^{7 + 3} c^{5} \cdot c^{2}$

Add $7$ and $3$ .

$a^{3} b^{10} c^{5} \cdot c^{2}$

Step 3

Multiply $c^{5}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

$a^{3} b^{10} (c^{2} c^{5})$

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

$a^{3} b^{10} c^{2 + 5}$

Add $2$ and $5$ .

$a^{3} b^{10} c^{7}$