Simplify ((4x^20)/(2x^5))((100x^20)/(25x^5))((2x^20)/(2x^5))

$(\frac{4 x^{20}}{2 x^{5}}) (\frac{100 x^{20}}{25 x^{5}}) (\frac{2 x^{20}}{2 x^{5}})$

Step 1

Combine.

$\frac{4 x^{20} (100 x^{20})}{2 x^{5} (25 x^{5})} \cdot \frac{2 x^{20}}{2 x^{5}}$

Step 2

Combine.

$\frac{4 x^{20} (100 x^{20}) (2 x^{20})}{2 x^{5} (25 x^{5}) (2 x^{5})}$

Step 3

Multiply $x^{20}$ by $x^{20}$ by adding the exponents.

Move $x^{20}$ .

$\frac{4 (x^{20} x^{20}) \cdot 100 (2 x^{20})}{2 x^{5} (25 x^{5}) (2 x^{5})}$

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

$\frac{4 x^{20 + 20} \cdot 100 (2 x^{20})}{2 x^{5} (25 x^{5}) (2 x^{5})}$

Add $20$ and $20$ .

$\frac{4 x^{40} \cdot 100 (2 x^{20})}{2 x^{5} (25 x^{5}) (2 x^{5})}$

Step 4

Multiply $x^{40}$ by $x^{20}$ by adding the exponents.

Move $x^{20}$ .

$\frac{4 (x^{20} x^{40}) \cdot 100 \cdot 2}{2 x^{5} (25 x^{5}) (2 x^{5})}$

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

$\frac{4 x^{20 + 40} \cdot 100 \cdot 2}{2 x^{5} (25 x^{5}) (2 x^{5})}$

Add $20$ and $40$ .

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 x^{5} (25 x^{5}) (2 x^{5})}$

Step 5

Multiply $x^{5}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 (x^{5} x^{5}) \cdot 25 (2 x^{5})}$

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

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 x^{5 + 5} \cdot 25 (2 x^{5})}$

Add $5$ and $5$ .

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 x^{10} \cdot 25 (2 x^{5})}$

Step 6

Multiply $x^{10}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 (x^{5} x^{10}) \cdot 25 \cdot 2}$

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

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 x^{5 + 10} \cdot 25 \cdot 2}$

Add $5$ and $10$ .

$\frac{4 x^{60} \cdot 100 \cdot 2}{2 x^{15} \cdot 25 \cdot 2}$

Step 7

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x^{60} \cdot 100 \cdot 2$ .

$\frac{2 (2 x^{60} \cdot 100 \cdot 2)}{2 x^{15} \cdot 25 \cdot 2}$

Cancel the common factors.

Factor $2$ out of $2 x^{15} \cdot 25 \cdot 2$ .

$\frac{2 (2 x^{60} \cdot 100 \cdot 2)}{2 (x^{15} \cdot 25 \cdot 2)}$

Cancel the common factor.

$\frac{2 (2 x^{60} \cdot 100 \cdot 2)}{2 (x^{15} \cdot 25 \cdot 2)}$

Rewrite the expression.

$\frac{2 x^{60} \cdot 100 \cdot 2}{x^{15} \cdot 25 \cdot 2}$

Step 8

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{60} \cdot 100 \cdot 2}{x^{15} \cdot 25 \cdot 2}$

Rewrite the expression.

$\frac{x^{60} \cdot 100 \cdot 2}{x^{15} \cdot 25}$

Step 9

Cancel the common factor of $x^{60}$ and $x^{15}$ .

Factor $x^{15}$ out of $x^{60} \cdot 100 \cdot 2$ .

$\frac{x^{15} (x^{45} \cdot 100 \cdot 2)}{x^{15} \cdot 25}$

Cancel the common factors.

Factor $x^{15}$ out of $x^{15} \cdot 25$ .

$\frac{x^{15} (x^{45} \cdot 100 \cdot 2)}{x^{15} (25)}$

Cancel the common factor.

$\frac{x^{15} (x^{45} \cdot 100 \cdot 2)}{x^{15} \cdot 25}$

Rewrite the expression.

$\frac{x^{45} \cdot 100 \cdot 2}{25}$

Step 10

Cancel the common factor of $100$ and $25$ .

Factor $25$ out of $x^{45} \cdot 100 \cdot 2$ .

$\frac{25 (x^{45} \cdot 4 \cdot 2)}{25}$

Cancel the common factors.

Factor $25$ out of $25$ .

$\frac{25 (x^{45} \cdot 4 \cdot 2)}{25 (1)}$

Cancel the common factor.

$\frac{25 (x^{45} \cdot 4 \cdot 2)}{25 \cdot 1}$

Rewrite the expression.

$\frac{x^{45} \cdot 4 \cdot 2}{1}$

Divide $x^{45} \cdot 4 \cdot 2$ by $1$ .

$x^{45} \cdot 4 \cdot 2$

Step 11

Simplify the expression.

Move $4$ to the left of $x^{45}$ .

$4 \cdot x^{45} \cdot 2$

Multiply $2$ by $4$ .

$8 x^{45}$

Simplify ((4x^20)/(2x^5))((100x^20)/(25x^5))((2x^20)/(2x^5))

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