Algebra Examples

$\frac{{(- 4)}^{3} \cdot 3^{7} \cdot 12}{6^{6} \cdot 2^{5}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{- 64 \cdot 3^{7} \cdot 12}{6^{6} \cdot 2^{5}}$

Step 1.2

Raise $3$ to the power of $7$ .

$\frac{- 64 \cdot 2187 \cdot 12}{6^{6} \cdot 2^{5}}$

Step 1.3

Combine exponents.

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Step 1.3.1

Multiply $- 64$ by $2187$ .

$\frac{- 139968 \cdot 12}{6^{6} \cdot 2^{5}}$

Step 1.3.2

Multiply $- 139968$ by $12$ .

$\frac{- 1679616}{6^{6} \cdot 2^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{- 1679616}{46656 \cdot 2^{5}}$

Step 2.2

Raise $2$ to the power of $5$ .

$\frac{- 1679616}{46656 \cdot 32}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $46656$ by $32$ .

$\frac{- 1679616}{1492992}$

Step 3.2

Cancel the common factor of $- 1679616$ and $1492992$ .

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Step 3.2.1

Factor $186624$ out of $- 1679616$ .

$\frac{186624 (- 9)}{1492992}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $186624$ out of $1492992$ .

$\frac{186624 \cdot - 9}{186624 \cdot 8}$

Step 3.2.2.2

Cancel the common factor.

$\frac{186624 \cdot - 9}{186624 \cdot 8}$

Step 3.2.2.3

Rewrite the expression.

$\frac{- 9}{8}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{9}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{8}$

Decimal Form:

$- 1.125$

Mixed Number Form:

$- 1 \frac{1}{8}$