Simplify (10(bc)^2)/(c square root of 16b^4)

$\frac{10 {(b c)}^{2}}{c \sqrt{16 b^{4}}}$

Step 1

Apply the product rule to $b c$ .

$\frac{10 b^{2} c^{2}}{c \sqrt{16 b^{4}}}$

Step 2

Simplify the denominator.

Rewrite $16 b^{4}$ as ${(4 b^{2})}^{2}$ .

$\frac{10 b^{2} c^{2}}{c \sqrt{{(4 b^{2})}^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{10 b^{2} c^{2}}{c \cdot 4 b^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10 b^{2} c^{2}$ .

$\frac{2 (5 b^{2} c^{2})}{c \cdot 4 b^{2}}$

Cancel the common factors.

Factor $2$ out of $c \cdot 4 b^{2}$ .

$\frac{2 (5 b^{2} c^{2})}{2 (c \cdot 2 b^{2})}$

Cancel the common factor.

$\frac{2 (5 b^{2} c^{2})}{2 (c \cdot 2 b^{2})}$

Rewrite the expression.

$\frac{5 b^{2} c^{2}}{c \cdot 2 b^{2}}$

Cancel the common factor of $b^{2}$ .

Cancel the common factor.

$\frac{5 b^{2} c^{2}}{c \cdot 2 b^{2}}$

Rewrite the expression.

$\frac{5 c^{2}}{c \cdot 2}$

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

Factor $c$ out of $5 c^{2}$ .

$\frac{c (5 c)}{c \cdot 2}$

Cancel the common factors.

Factor $c$ out of $c \cdot 2$ .

$\frac{c (5 c)}{c (2)}$

Cancel the common factor.

$\frac{c (5 c)}{c \cdot 2}$

Rewrite the expression.

$\frac{5 c}{2}$