Simplify (4h^3k^2)/7*(21hk^5)/2

$\frac{4 h^{3} k^{2}}{7} \cdot \frac{21 h k^{5}}{2}$

Combine.

$\frac{4 h^{3} k^{2} (21 h k^{5})}{7 \cdot 2}$

Multiply $h^{3}$ by $h$ by adding the exponents.

Move $h$ .

$\frac{4 (h \cdot h^{3}) k^{2} (21 k^{5})}{7 \cdot 2}$

Multiply $h$ by $h^{3}$ .

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

$\frac{4 (h^{1} h^{3}) k^{2} (21 k^{5})}{7 \cdot 2}$

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

$\frac{4 h^{1 + 3} k^{2} (21 k^{5})}{7 \cdot 2}$

Add $1$ and $3$ .

$\frac{4 h^{4} k^{2} (21 k^{5})}{7 \cdot 2}$

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

Move $k^{5}$ .

$\frac{4 h^{4} (k^{5} k^{2}) \cdot 21}{7 \cdot 2}$

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

$\frac{4 h^{4} k^{5 + 2} \cdot 21}{7 \cdot 2}$

Add $5$ and $2$ .

$\frac{4 h^{4} k^{7} \cdot 21}{7 \cdot 2}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 h^{4} k^{7} \cdot 21$ .

$\frac{2 (2 h^{4} k^{7} \cdot 21)}{7 \cdot 2}$

Cancel the common factors.

Factor $2$ out of $7 \cdot 2$ .

$\frac{2 (2 h^{4} k^{7} \cdot 21)}{2 \cdot 7}$

Cancel the common factor.

$\frac{2 (2 h^{4} k^{7} \cdot 21)}{2 \cdot 7}$

Rewrite the expression.

$\frac{2 h^{4} k^{7} \cdot 21}{7}$

Cancel the common factor of $21$ and $7$ .

Factor $7$ out of $2 h^{4} k^{7} \cdot 21$ .

$\frac{7 (2 h^{4} k^{7} \cdot 3)}{7}$

Cancel the common factors.

Factor $7$ out of $7$ .

$\frac{7 (2 h^{4} k^{7} \cdot 3)}{7 (1)}$

Cancel the common factor.

$\frac{7 (2 h^{4} k^{7} \cdot 3)}{7 \cdot 1}$

Rewrite the expression.

$\frac{2 h^{4} k^{7} \cdot 3}{1}$

Divide $2 h^{4} k^{7} \cdot 3$ by $1$ .

$2 h^{4} k^{7} \cdot 3$

Multiply $3$ by $2$ .

$6 h^{4} k^{7}$