Simplify (10a^4b^6)(3a^5b^2)-7a^9b^8

$(10 a^{4} b^{6}) (3 a^{5} b^{2}) - 7 a^{9} b^{8}$

Step 1

Simplify each term.

Multiply $a^{4}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$10 (a^{5} a^{4}) b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

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

$10 a^{5 + 4} b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

Add $5$ and $4$ .

$10 a^{9} b^{6} (3 b^{2}) - 7 a^{9} b^{8}$

Multiply $b^{6}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$10 a^{9} (b^{2} b^{6}) \cdot 3 - 7 a^{9} b^{8}$

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

$10 a^{9} b^{2 + 6} \cdot 3 - 7 a^{9} b^{8}$

Add $2$ and $6$ .

$10 a^{9} b^{8} \cdot 3 - 7 a^{9} b^{8}$

Multiply $3$ by $10$ .

$30 a^{9} b^{8} - 7 a^{9} b^{8}$

Step 2

Subtract $7 a^{9} b^{8}$ from $30 a^{9} b^{8}$ .

$23 a^{9} b^{8}$