Simplify 8^(2n-3n+2(n-4^(2n)))

$8^{2 n - 3 n + 2 (n - 4^{2 n})}$

Simplify each term.

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Apply the distributive property.

$8^{2 n - 3 n + 2 n + 2 (- 4^{2 n})}$

Multiply $2 (- 4^{2 n})$ .

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Multiply $- 1$ by $2$ .

$8^{2 n - 3 n + 2 n - 2 \cdot 4^{2 n}}$

Factor out negative.

$8^{2 n - 3 n + 2 n - (2 \cdot 4^{2 n})}$

Rewrite $4$ as $2^{2}$ .

$8^{2 n - 3 n + 2 n - (2 \cdot {(2^{2})}^{2 n})}$

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

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

$8^{2 n - 3 n + 2 n - (2 \cdot 2^{2 (2 n)})}$

Multiply $2$ by $2$ .

$8^{2 n - 3 n + 2 n - (2 \cdot 2^{4 n})}$

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

$8^{2 n - 3 n + 2 n - 2^{1 + 4 n}}$

Simplify by adding terms.

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Subtract $3 n$ from $2 n$ .

$8^{- n + 2 n - 2^{1 + 4 n}}$

Add $- n$ and $2 n$ .

$8^{n - 2^{1 + 4 n}}$

Simplify 8^(2n-3n+2(n-4^(2n)))

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