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

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

Step 1

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

Apply the product rule to $3 x^{2} y^{6}$ .

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

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

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

Step 2

Raise $3$ to the power of $7$ .

$2187 {(x^{2})}^{7} {(y^{6})}^{7}$

Step 3

Multiply the exponents in ${(x^{2})}^{7}$ .

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

$2187 x^{2 \cdot 7} {(y^{6})}^{7}$

Multiply $2$ by $7$ .

$2187 x^{14} {(y^{6})}^{7}$

Step 4

Multiply the exponents in ${(y^{6})}^{7}$ .

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

$2187 x^{14} y^{6 \cdot 7}$

Multiply $6$ by $7$ .

$2187 x^{14} y^{42}$