Simplify (4a^3c^2)^3(-3ac^4)^2

${(4 a^{3} c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $4 a^{3} c^{2}$ .

${(4 a^{3})}^{3} {(c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Apply the product rule to $4 a^{3}$ .

$4^{3} {(a^{3})}^{3} {(c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Step 2

Raise $4$ to the power of $3$ .

$64 {(a^{3})}^{3} {(c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Step 3

Multiply the exponents in ${(a^{3})}^{3}$ .

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

$64 a^{3 \cdot 3} {(c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Multiply $3$ by $3$ .

$64 a^{9} {(c^{2})}^{3} {(- 3 a c^{4})}^{2}$

Step 4

Multiply the exponents in ${(c^{2})}^{3}$ .

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

$64 a^{9} c^{2 \cdot 3} {(- 3 a c^{4})}^{2}$

Multiply $2$ by $3$ .

$64 a^{9} c^{6} {(- 3 a c^{4})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- 3 a c^{4}$ .

$64 a^{9} c^{6} ({(- 3 a)}^{2} {(c^{4})}^{2})$

Apply the product rule to $- 3 a$ .

$64 a^{9} c^{6} ({(- 3)}^{2} a^{2} {(c^{4})}^{2})$

Step 6

Multiply $a^{9}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$64 (a^{2} a^{9}) c^{6} ({(- 3)}^{2} {(c^{4})}^{2})$

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

$64 a^{2 + 9} c^{6} ({(- 3)}^{2} {(c^{4})}^{2})$

Add $2$ and $9$ .

$64 a^{11} c^{6} ({(- 3)}^{2} {(c^{4})}^{2})$

Step 7

Raise $- 3$ to the power of $2$ .

$64 a^{11} c^{6} (9 {(c^{4})}^{2})$

Step 8

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

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

$64 a^{11} c^{6} (9 c^{4 \cdot 2})$

Multiply $4$ by $2$ .

$64 a^{11} c^{6} (9 c^{8})$

Step 9

Multiply $c^{6}$ by $c^{8}$ by adding the exponents.

Move $c^{8}$ .

$64 a^{11} (c^{8} c^{6}) \cdot 9$

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

$64 a^{11} c^{8 + 6} \cdot 9$

Add $8$ and $6$ .

$64 a^{11} c^{14} \cdot 9$

Step 10

Multiply $9$ by $64$ .

$576 a^{11} c^{14}$

Simplify (4a^3c^2)^3(-3ac^4)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.