Simplify (7/6a^7b^2)(5a^4b^6)

$(\frac{7}{6} a^{7} b^{2}) (5 a^{4} b^{6})$

Step 1

Multiply $a^{7}$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$\frac{7}{6} \cdot (a^{4} a^{7} b^{2}) (5 b^{6})$

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

$\frac{7}{6} \cdot (a^{4 + 7} b^{2}) (5 b^{6})$

Add $4$ and $7$ .

$\frac{7}{6} \cdot (a^{11} b^{2}) (5 b^{6})$

Step 2

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

Move $b^{6}$ .

$\frac{7}{6} \cdot (a^{11} (b^{6} b^{2})) \cdot 5$

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

$\frac{7}{6} \cdot (a^{11} b^{6 + 2}) \cdot 5$

Add $6$ and $2$ .

$\frac{7}{6} \cdot (a^{11} b^{8}) \cdot 5$

Step 3

Multiply $\frac{7}{6} (a^{11} b^{8})$ .

Combine $a^{11}$ and $\frac{7}{6}$ .

$\frac{a^{11} \cdot 7}{6} b^{8} \cdot 5$

Combine $\frac{a^{11} \cdot 7}{6}$ and $b^{8}$ .

$\frac{a^{11} \cdot 7 b^{8}}{6} \cdot 5$

Step 4

Move $7$ to the left of $a^{11}$ .

$\frac{7 \cdot a^{11} b^{8}}{6} \cdot 5$

Step 5

Multiply $\frac{7 a^{11} b^{8}}{6} \cdot 5$ .

Combine $\frac{7 a^{11} b^{8}}{6}$ and $5$ .

$\frac{7 a^{11} b^{8} \cdot 5}{6}$

Multiply $5$ by $7$ .

$\frac{35 a^{11} b^{8}}{6}$