Simplify (2(fg^4))^4(fg)^6

${(2 (f g^{4}))}^{4} {(f g)}^{6}$

Step 1

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

Apply the product rule to $2 f g^{4}$ .

${(2 f)}^{4} {(g^{4})}^{4} {(f g)}^{6}$

Apply the product rule to $2 f$ .

$2^{4} f^{4} {(g^{4})}^{4} {(f g)}^{6}$

Step 2

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

$16 f^{4} {(g^{4})}^{4} {(f g)}^{6}$

Step 3

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

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

$16 f^{4} g^{4 \cdot 4} {(f g)}^{6}$

Multiply $4$ by $4$ .

$16 f^{4} g^{16} {(f g)}^{6}$

Step 4

Apply the product rule to $f g$ .

$16 f^{4} g^{16} (f^{6} g^{6})$

Step 5

Multiply $f^{4}$ by $f^{6}$ by adding the exponents.

Move $f^{6}$ .

$16 (f^{6} f^{4}) g^{16} g^{6}$

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

$16 f^{6 + 4} g^{16} g^{6}$

Add $6$ and $4$ .

$16 f^{10} g^{16} g^{6}$

Step 6

Multiply $g^{16}$ by $g^{6}$ by adding the exponents.

Move $g^{6}$ .

$16 f^{10} (g^{6} g^{16})$

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

$16 f^{10} g^{6 + 16}$

Add $6$ and $16$ .

$16 f^{10} g^{22}$