Evaluate ((32^25-72^24)52)/((-8)^3(32^20+72^19))

$\frac{(3 \cdot 2^{25} - 7 \cdot 2^{24}) \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Simplify the numerator.

Raise $2$ to the power of $25$ .

$\frac{(3 \cdot 33554432 - 7 \cdot 2^{24}) \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Multiply $3$ by $33554432$ .

$\frac{(100663296 - 7 \cdot 2^{24}) \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Raise $2$ to the power of $24$ .

$\frac{(100663296 - 7 \cdot 16777216) \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Multiply $- 7$ by $16777216$ .

$\frac{(100663296 - 117440512) \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Subtract $117440512$ from $100663296$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} \cdot (3 \cdot 2^{20} + 7 \cdot 2^{19})}$

Simplify the denominator.

Raise $2$ to the power of $20$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} (3 \cdot 1048576 + 7 \cdot 2^{19})}$

Multiply $3$ by $1048576$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} (3145728 + 7 \cdot 2^{19})}$

Raise $2$ to the power of $19$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} (3145728 + 7 \cdot 524288)}$

Multiply $7$ by $524288$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} (3145728 + 3670016)}$

Add $3145728$ and $3670016$ .

$\frac{- 16777216 \cdot 52}{{(- 8)}^{3} \cdot 6815744}$

Raise $- 8$ to the power of $3$ .

$\frac{- 16777216 \cdot 52}{- 512 \cdot 6815744}$

Reduce the expression by cancelling the common factors.

Multiply $- 16777216$ by $52$ .

$\frac{- 872415232}{- 512 \cdot 6815744}$

Multiply $- 512$ by $6815744$ .

$\frac{- 872415232}{- 3489660928}$

Cancel the common factor of $- 872415232$ and $- 3489660928$ .

Factor $- 872415232$ out of $- 872415232$ .

$\frac{- 872415232 (1)}{- 3489660928}$

Cancel the common factors.

Factor $- 872415232$ out of $- 3489660928$ .

$\frac{- 872415232 \cdot 1}{- 872415232 \cdot 4}$

Cancel the common factor.

$\frac{- 872415232 \cdot 1}{- 872415232 \cdot 4}$

Rewrite the expression.

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

Evaluate ((3*2^25-7*2^24)*52)/((-8)^3*(3*2^20+7*2^19))

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Evaluate ((32^25-72^24)52)/((-8)^3(32^20+72^19))