Simplify (-8m^4n^7)^2-(2m^2n)^3*(5m^2n^11)

${(- 8 m^{4} n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Step 1

Simplify each term.

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

Apply the product rule to $- 8 m^{4} n^{7}$ .

${(- 8 m^{4})}^{2} {(n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Apply the product rule to $- 8 m^{4}$ .

${(- 8)}^{2} {(m^{4})}^{2} {(n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Raise $- 8$ to the power of $2$ .

$64 {(m^{4})}^{2} {(n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

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

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

$64 m^{4 \cdot 2} {(n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Multiply $4$ by $2$ .

$64 m^{8} {(n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Multiply the exponents in ${(n^{7})}^{2}$ .

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

$64 m^{8} n^{7 \cdot 2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

Multiply $7$ by $2$ .

$64 m^{8} n^{14} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$

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

Apply the product rule to $2 m^{2} n$ .

$64 m^{8} n^{14} - ({(2 m^{2})}^{3} n^{3}) \cdot (5 m^{2} n^{11})$

Apply the product rule to $2 m^{2}$ .

$64 m^{8} n^{14} - (2^{3} {(m^{2})}^{3} n^{3}) \cdot (5 m^{2} n^{11})$

Multiply $n^{3}$ by $n^{11}$ by adding the exponents.

Move $n^{11}$ .

$64 m^{8} n^{14} - (2^{3} {(m^{2})}^{3} (n^{11} n^{3})) \cdot (5 m^{2})$

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

$64 m^{8} n^{14} - (2^{3} {(m^{2})}^{3} n^{11 + 3}) \cdot (5 m^{2})$

Add $11$ and $3$ .

$64 m^{8} n^{14} - (2^{3} {(m^{2})}^{3} n^{14}) \cdot (5 m^{2})$

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

$64 m^{8} n^{14} - (8 {(m^{2})}^{3} n^{14}) \cdot (5 m^{2})$

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

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

$64 m^{8} n^{14} - (8 m^{2 \cdot 3} n^{14}) \cdot (5 m^{2})$

Multiply $2$ by $3$ .

$64 m^{8} n^{14} - (8 m^{6} n^{14}) \cdot (5 m^{2})$

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

Move $m^{2}$ .

$64 m^{8} n^{14} - (8 (m^{2} m^{6}) n^{14}) \cdot 5$

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

$64 m^{8} n^{14} - (8 m^{2 + 6} n^{14}) \cdot 5$

Add $2$ and $6$ .

$64 m^{8} n^{14} - (8 m^{8} n^{14}) \cdot 5$

Multiply $8$ by $- 1$ .

$64 m^{8} n^{14} - 8 (m^{8} n^{14}) \cdot 5$

Multiply $5$ by $- 8$ .

$64 m^{8} n^{14} - 40 m^{8} n^{14}$

Step 2

Subtract $40 m^{8} n^{14}$ from $64 m^{8} n^{14}$ .

$24 m^{8} n^{14}$

Simplify (-8m^4n^7)^2-(2m^2n)^3*(5m^2n^11)

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