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

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

Step 1

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

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

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

Multiply $2$ by $3$ .

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

Step 2

Multiply the exponents in ${(y^{2})}^{4}$ .

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

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

Multiply $2$ by $4$ .

$x^{6} y^{8} {(x^{3})}^{7}$

Step 3

Multiply the exponents in ${(x^{3})}^{7}$ .

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

$x^{6} y^{8} x^{3 \cdot 7}$

Multiply $3$ by $7$ .

$x^{6} y^{8} x^{21}$

Step 4

Multiply $x^{6}$ by $x^{21}$ by adding the exponents.

Move $x^{21}$ .

$x^{21} x^{6} y^{8}$

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

$x^{21 + 6} y^{8}$

Add $21$ and $6$ .

$x^{27} y^{8}$