Simplify 3(2x^6y^7)^4

$3 {(2 x^{6} y^{7})}^{4}$

Step 1

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

Apply the product rule to $2 x^{6} y^{7}$ .

$3 ({(2 x^{6})}^{4} {(y^{7})}^{4})$

Apply the product rule to $2 x^{6}$ .

$3 (2^{4} {(x^{6})}^{4} {(y^{7})}^{4})$

Step 2

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

$3 (16 {(x^{6})}^{4} {(y^{7})}^{4})$

Step 3

Multiply the exponents in ${(x^{6})}^{4}$ .

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

$3 (16 x^{6 \cdot 4} {(y^{7})}^{4})$

Multiply $6$ by $4$ .

$3 (16 x^{24} {(y^{7})}^{4})$

Step 4

Multiply the exponents in ${(y^{7})}^{4}$ .

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

$3 (16 x^{24} y^{7 \cdot 4})$

Multiply $7$ by $4$ .

$3 (16 x^{24} y^{28})$

Step 5

Multiply $16$ by $3$ .

$48 x^{24} y^{28}$