Simplify (ab)(6a^5b)(-ab)

$(a b) (6 a^{5} b) (- a b)$

Step 1

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

Move $a^{5}$ .

$a^{5} a b (6 b) (- a b)$

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

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

$a^{5} a^{1} b (6 b) (- a b)$

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

$a^{5 + 1} b (6 b) (- a b)$

Add $5$ and $1$ .

$a^{6} b (6 b) (- a b)$

Step 2

Multiply $a^{6}$ by $a$ by adding the exponents.

Move $a$ .

$a \cdot a^{6} b (6 b) (- 1 b)$

Multiply $a$ by $a^{6}$ .

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

$a^{1} a^{6} b (6 b) (- 1 b)$

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

$a^{1 + 6} b (6 b) (- 1 b)$

Add $1$ and $6$ .

$a^{7} b (6 b) (- 1 b)$

Step 3

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$a^{7} (b \cdot b) \cdot 6 (- 1 b)$

Multiply $b$ by $b$ .

$a^{7} b^{2} \cdot 6 (- 1 b)$

Step 4

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

Move $b$ .

$a^{7} (b \cdot b^{2}) \cdot 6 \cdot - 1$

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

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

$a^{7} (b^{1} b^{2}) \cdot 6 \cdot - 1$

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

$a^{7} b^{1 + 2} \cdot 6 \cdot - 1$

Add $1$ and $2$ .

$a^{7} b^{3} \cdot 6 \cdot - 1$

Step 5

Move $6$ to the left of $a^{7} b^{3}$ .

$6 \cdot (a^{7} b^{3}) \cdot - 1$

Step 6

Multiply $- 1$ by $6$ .

$- 6 a^{7} b^{3}$

Simplify (ab)(6a^5b)(-ab)

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