Simplify 2.5/(2a^2)*(4a^3)/(5b^2)

$\frac{2.5}{2 a^{2}} \cdot \frac{4 a^{3}}{5 b^{2}}$

Step 1

Combine.

$\frac{2.5 (4 a^{3})}{2 a^{2} (5 b^{2})}$

Step 2

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

Factor $2$ out of $2.5 (4 a^{3})$ .

$\frac{2 (1.25 (4 a^{3}))}{2 a^{2} (5 b^{2})}$

Cancel the common factors.

Factor $2$ out of $2 a^{2} (5 b^{2})$ .

$\frac{2 (1.25 (4 a^{3}))}{2 (a^{2} (5 b^{2}))}$

Cancel the common factor.

$\frac{2 (1.25 (4 a^{3}))}{2 (a^{2} (5 b^{2}))}$

Rewrite the expression.

$\frac{1.25 (4 a^{3})}{a^{2} (5 b^{2})}$

$\frac{1.25 (4 a^{3})}{a^{2} (5 b^{2})}$

$\frac{1.25 (4 a^{3})}{a^{2} (5 b^{2})}$

Step 3

Cancel the common factor of $a^{3}$ and $a^{2}$ .

Factor $a^{2}$ out of $1.25 (4 a^{3})$ .

$\frac{a^{2} (1.25 (4 a))}{a^{2} (5 b^{2})}$

Cancel the common factors.

Cancel the common factor.

$\frac{a^{2} (1.25 (4 a))}{a^{2} (5 b^{2})}$

Rewrite the expression.

$\frac{1.25 (4 a)}{5 b^{2}}$

$\frac{1.25 (4 a)}{5 b^{2}}$

$\frac{1.25 (4 a)}{5 b^{2}}$

Step 4

Multiply $1.25$ by $4$ .

$\frac{5 a}{5 b^{2}}$

Step 5

Cancel the common factor of $5$ and $5$ .

Cancel the common factor.

$\frac{5 a}{5 b^{2}}$

Rewrite the expression.

$\frac{a}{b^{2}}$

$\frac{a}{b^{2}}$

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