Simplify (5v^4)^22v^3v

${(5 v^{4})}^{2} \cdot 2 v^{3} \cdot v$

Step 1

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

Move $v$ .

${(5 v^{4})}^{2} \cdot (2 (v \cdot v^{3}))$

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

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

${(5 v^{4})}^{2} \cdot (2 (v^{1} v^{3}))$

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

${(5 v^{4})}^{2} \cdot (2 v^{1 + 3})$

Add $1$ and $3$ .

${(5 v^{4})}^{2} \cdot (2 v^{4})$

Step 2

Rewrite using the commutative property of multiplication.

$2 {(5 v^{4})}^{2} v^{4}$

Step 3

Apply the product rule to $5 v^{4}$ .

$2 (5^{2} {(v^{4})}^{2}) v^{4}$

Step 4

Raise $5$ to the power of $2$ .

$2 (25 {(v^{4})}^{2}) v^{4}$

Step 5

Multiply the exponents in ${(v^{4})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (25 v^{4 \cdot 2}) v^{4}$

Multiply $4$ by $2$ .

$2 (25 v^{8}) v^{4}$

Step 6

Multiply $v^{8}$ by $v^{4}$ by adding the exponents.

Move $v^{4}$ .

$2 (25 (v^{4} v^{8}))$

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

$2 (25 v^{4 + 8})$

Add $4$ and $8$ .

$2 (25 v^{12})$

Step 7

Multiply $25$ by $2$ .

$50 v^{12}$

Simplify (5v^4)^2*2v^3*v