Simplify (5ax^2)(a^2x^3)(6ax)

$(5 a x^{2}) (a^{2} x^{3}) (6 a x)$

Step 1

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

Move $a^{2}$ .

$5 (a^{2} a) x^{2} x^{3} (6 a x)$

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

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

$5 (a^{2} a^{1}) x^{2} x^{3} (6 a x)$

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

$5 a^{2 + 1} x^{2} x^{3} (6 a x)$

Add $2$ and $1$ .

$5 a^{3} x^{2} x^{3} (6 a x)$

Step 2

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

Move $a$ .

$5 (a \cdot a^{3}) x^{2} x^{3} (6 x)$

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

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

$5 (a^{1} a^{3}) x^{2} x^{3} (6 x)$

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

$5 a^{1 + 3} x^{2} x^{3} (6 x)$

Add $1$ and $3$ .

$5 a^{4} x^{2} x^{3} (6 x)$

Step 3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$5 a^{4} (x^{3} x^{2}) (6 x)$

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

$5 a^{4} x^{3 + 2} (6 x)$

Add $3$ and $2$ .

$5 a^{4} x^{5} (6 x)$

Step 4

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

Move $x$ .

$5 a^{4} (x \cdot x^{5}) \cdot 6$

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

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

$5 a^{4} (x^{1} x^{5}) \cdot 6$

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

$5 a^{4} x^{1 + 5} \cdot 6$

Add $1$ and $5$ .

$5 a^{4} x^{6} \cdot 6$

Step 5

Multiply $6$ by $5$ .

$30 a^{4} x^{6}$