Simplify ((2cd^4)^4)/((2c^2d^3)^2)

$\frac{{(2 c d^{4})}^{4}}{{(2 c^{2} d^{3})}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $2 c d^{4}$ .

$\frac{{(2 c)}^{4} {(d^{4})}^{4}}{{(2 c^{2} d^{3})}^{2}}$

Apply the product rule to $2 c$ .

$\frac{2^{4} c^{4} {(d^{4})}^{4}}{{(2 c^{2} d^{3})}^{2}}$

Raise $2$ to the power of $4$ .

$\frac{16 c^{4} {(d^{4})}^{4}}{{(2 c^{2} d^{3})}^{2}}$

Multiply the exponents in ${(d^{4})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{16 c^{4} d^{4 \cdot 4}}{{(2 c^{2} d^{3})}^{2}}$

Multiply $4$ by $4$ .

$\frac{16 c^{4} d^{16}}{{(2 c^{2} d^{3})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 c^{2} d^{3}$ .

$\frac{16 c^{4} d^{16}}{{(2 c^{2})}^{2} {(d^{3})}^{2}}$

Apply the product rule to $2 c^{2}$ .

$\frac{16 c^{4} d^{16}}{2^{2} {(c^{2})}^{2} {(d^{3})}^{2}}$

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

$\frac{16 c^{4} d^{16}}{4 {(c^{2})}^{2} {(d^{3})}^{2}}$

Multiply the exponents in ${(c^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{16 c^{4} d^{16}}{4 c^{2 \cdot 2} {(d^{3})}^{2}}$

Multiply $2$ by $2$ .

$\frac{16 c^{4} d^{16}}{4 c^{4} {(d^{3})}^{2}}$

Multiply the exponents in ${(d^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{16 c^{4} d^{16}}{4 c^{4} d^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{16 c^{4} d^{16}}{4 c^{4} d^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $16$ and $4$ .

Factor $4$ out of $16 c^{4} d^{16}$ .

$\frac{4 (4 c^{4} d^{16})}{4 c^{4} d^{6}}$

Cancel the common factors.

Factor $4$ out of $4 c^{4} d^{6}$ .

$\frac{4 (4 c^{4} d^{16})}{4 (c^{4} d^{6})}$

Cancel the common factor.

$\frac{4 (4 c^{4} d^{16})}{4 (c^{4} d^{6})}$

Rewrite the expression.

$\frac{4 c^{4} d^{16}}{c^{4} d^{6}}$

Cancel the common factor of $c^{4}$ .

Cancel the common factor.

$\frac{4 c^{4} d^{16}}{c^{4} d^{6}}$

Rewrite the expression.

$\frac{4 d^{16}}{d^{6}}$

Cancel the common factor of $d^{16}$ and $d^{6}$ .

Factor $d^{6}$ out of $4 d^{16}$ .

$\frac{d^{6} (4 d^{10})}{d^{6}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{d^{6} (4 d^{10})}{d^{6} \cdot 1}$

Cancel the common factor.

$\frac{d^{6} (4 d^{10})}{d^{6} \cdot 1}$

Rewrite the expression.

$\frac{4 d^{10}}{1}$

Divide $4 d^{10}$ by $1$ .

$4 d^{10}$

Simplify ((2cd^4)^4)/((2c^2d^3)^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.