Evaluate ((4^-3)^-2((4^4)^3))/((4^-4)^-5)

$\frac{{(4^{- 3})}^{- 2} ({(4^{4})}^{3})}{{(4^{- 4})}^{- 5}}$

Simplify.

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Move ${(4^{- 3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(4^{4})}^{3}}{{(4^{- 4})}^{- 5} {(4^{- 3})}^{2}}$

Move ${(4^{- 4})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(4^{4})}^{3} {(4^{- 4})}^{5}}{{(4^{- 3})}^{2}}$

Simplify the numerator.

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Multiply the exponents in ${(4^{4})}^{3}$ .

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

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

Multiply $4$ by $3$ .

$\frac{4^{12} {(4^{- 4})}^{5}}{{(4^{- 3})}^{2}}$

Raise $4$ to the power of $12$ .

$\frac{16777216 {(4^{- 4})}^{5}}{{(4^{- 3})}^{2}}$

Multiply the exponents in ${(4^{- 4})}^{5}$ .

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

$\frac{16777216 \cdot 4^{- 4 \cdot 5}}{{(4^{- 3})}^{2}}$

Multiply $- 4$ by $5$ .

$\frac{16777216 \cdot 4^{- 20}}{{(4^{- 3})}^{2}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{16777216 \frac{1}{4^{20}}}{{(4^{- 3})}^{2}}$

Raise $4$ to the power of $20$ .

$\frac{16777216 (\frac{1}{1099511627776})}{{(4^{- 3})}^{2}}$

Simplify the denominator.

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Multiply the exponents in ${(4^{- 3})}^{2}$ .

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

$\frac{16777216 (\frac{1}{1099511627776})}{4^{- 3 \cdot 2}}$

Multiply $- 3$ by $2$ .

$\frac{16777216 (\frac{1}{1099511627776})}{4^{- 6}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{16777216 (\frac{1}{1099511627776})}{\frac{1}{4^{6}}}$

Raise $4$ to the power of $6$ .

$\frac{16777216 (\frac{1}{1099511627776})}{\frac{1}{4096}}$

Simplify terms.

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Combine $16777216$ and $\frac{1}{1099511627776}$ .

$\frac{\frac{16777216}{1099511627776}}{\frac{1}{4096}}$

Cancel the common factor of $16777216$ and $1099511627776$ .

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Factor $16777216$ out of $16777216$ .

$\frac{\frac{16777216 (1)}{1099511627776}}{\frac{1}{4096}}$

Cancel the common factors.

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Factor $16777216$ out of $1099511627776$ .

$\frac{\frac{16777216 \cdot 1}{16777216 \cdot 65536}}{\frac{1}{4096}}$

Cancel the common factor.

$\frac{\frac{16777216 \cdot 1}{16777216 \cdot 65536}}{\frac{1}{4096}}$

Rewrite the expression.

$\frac{\frac{1}{65536}}{\frac{1}{4096}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{65536} \cdot 4096$

Cancel the common factor of $4096$ .

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Factor $4096$ out of $65536$ .

$\frac{1}{4096 (16)} \cdot 4096$

Cancel the common factor.

$\frac{1}{4096 \cdot 16} \cdot 4096$

Rewrite the expression.

$\frac{1}{16}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$

Evaluate ((4^-3)^-2((4^4)^3))/((4^-4)^-5)

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