Simplify 4cd(2c^60d^4)^0

$4 c d {(2 c^{60} d^{4})}^{0}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 c^{60} d^{4}$ .

$4 c d ({(2 c^{60})}^{0} {(d^{4})}^{0})$

Apply the product rule to $2 c^{60}$ .

$4 c d (2^{0} {(c^{60})}^{0} {(d^{4})}^{0})$

Anything raised to $0$ is $1$ .

$4 c d (1 {(c^{60})}^{0} {(d^{4})}^{0})$

Multiply ${(c^{60})}^{0}$ by $1$ .

$4 c d ({(c^{60})}^{0} {(d^{4})}^{0})$

Multiply the exponents in ${(c^{60})}^{0}$ .

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

$4 c d (c^{60 \cdot 0} {(d^{4})}^{0})$

Multiply $60$ by $0$ .

$4 c d (c^{0} {(d^{4})}^{0})$

Multiply $c$ by $c^{0}$ by adding the exponents.

Move $c^{0}$ .

$4 (c^{0} c) d {(d^{4})}^{0}$

Multiply $c^{0}$ by $c$ .

Raise $c$ to the power of $1$ .

$4 (c^{0} c^{1}) d {(d^{4})}^{0}$

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

$4 c^{0 + 1} d {(d^{4})}^{0}$

Add $0$ and $1$ .

$4 c^{1} d {(d^{4})}^{0}$

Simplify $4 c^{1} d {(d^{4})}^{0}$ .

$4 c d$