Simplify ((-2)^85^3)/(5^42^10*10)

$\frac{{(- 2)}^{8} \cdot 5^{3}}{5^{4} \cdot 2^{10} \cdot 10}$

Step 1

Cancel the common factor of $5^{3}$ and $5^{4}$ .

Factor $5^{3}$ out of ${(- 2)}^{8} \cdot 5^{3}$ .

$\frac{5^{3} \cdot {(- 2)}^{8}}{5^{4} \cdot 2^{10} \cdot 10}$

Cancel the common factors.

Factor $5^{3}$ out of $5^{4} \cdot 2^{10} \cdot 10$ .

$\frac{5^{3} \cdot {(- 2)}^{8}}{5^{3} (5 \cdot 2^{10} \cdot 10)}$

Cancel the common factor.

$\frac{5^{3} \cdot {(- 2)}^{8}}{5^{3} (5 \cdot 2^{10} \cdot 10)}$

Rewrite the expression.

$\frac{{(- 2)}^{8}}{5 \cdot 2^{10} \cdot 10}$

Step 2

Cancel the common factor of ${(- 2)}^{8}$ and $2^{10}$ .

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{{(- 1 (2))}^{8}}{5 \cdot 2^{10} \cdot 10}$

Apply the product rule to $- 1 (2)$ .

$\frac{{(- 1)}^{8} \cdot 2^{8}}{5 \cdot 2^{10} \cdot 10}$

Raise $- 1$ to the power of $8$ .

$\frac{1 \cdot 2^{8}}{5 \cdot 2^{10} \cdot 10}$

Multiply $2^{8}$ by $1$ .

$\frac{2^{8}}{5 \cdot 2^{10} \cdot 10}$

Multiply by $1$ .

$\frac{2^{8} \cdot 1}{5 \cdot 2^{10} \cdot 10}$

Cancel the common factors.

Factor $2^{8}$ out of $5 \cdot 2^{10} \cdot 10$ .

$\frac{2^{8} \cdot 1}{2^{8} (5 \cdot 2^{2} \cdot 10)}$

Cancel the common factor.

$\frac{2^{8} \cdot 1}{2^{8} (5 \cdot 2^{2} \cdot 10)}$

Rewrite the expression.

$\frac{1}{5 \cdot 2^{2} \cdot 10}$

Step 3

Simplify the expression.

Multiply $10$ by $5$ .

$\frac{1}{50 \cdot 2^{2}}$

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

$\frac{1}{50 \cdot 4}$

Multiply $50$ by $4$ .

$\frac{1}{200}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{200}$

Decimal Form:

$0.005$

Simplify ((-2)^8*5^3)/(5^4*2^10*10)

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Simplify ((-2)^85^3)/(5^42^10*10)