Simplify (x^4y^3)^2*(x^3y^5)^3

${(x^{4} y^{3})}^{2} \cdot {(x^{3} y^{5})}^{3}$

Step 1

Apply the product rule to $x^{4} y^{3}$ .

${(x^{4})}^{2} {(y^{3})}^{2} \cdot {(x^{3} y^{5})}^{3}$

Step 2

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

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

$x^{4 \cdot 2} {(y^{3})}^{2} \cdot {(x^{3} y^{5})}^{3}$

Multiply $4$ by $2$ .

$x^{8} {(y^{3})}^{2} \cdot {(x^{3} y^{5})}^{3}$

Step 3

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

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

$x^{8} y^{3 \cdot 2} \cdot {(x^{3} y^{5})}^{3}$

Multiply $3$ by $2$ .

$x^{8} y^{6} \cdot {(x^{3} y^{5})}^{3}$

Step 4

Apply the product rule to $x^{3} y^{5}$ .

$x^{8} y^{6} \cdot ({(x^{3})}^{3} {(y^{5})}^{3})$

Step 5

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

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

$x^{8} y^{6} \cdot (x^{3 \cdot 3} {(y^{5})}^{3})$

Multiply $3$ by $3$ .

$x^{8} y^{6} \cdot (x^{9} {(y^{5})}^{3})$

Step 6

Multiply $x^{8}$ by $x^{9}$ by adding the exponents.

Move $x^{9}$ .

$x^{9} x^{8} y^{6} \cdot {(y^{5})}^{3}$

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

$x^{9 + 8} y^{6} \cdot {(y^{5})}^{3}$

Add $9$ and $8$ .

$x^{17} y^{6} \cdot {(y^{5})}^{3}$

Step 7

Multiply the exponents in ${(y^{5})}^{3}$ .

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

$x^{17} y^{6} \cdot y^{5 \cdot 3}$

Multiply $5$ by $3$ .

$x^{17} y^{6} \cdot y^{15}$

Step 8

Multiply $y^{6}$ by $y^{15}$ by adding the exponents.

Move $y^{15}$ .

$x^{17} (y^{15} y^{6})$

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

$x^{17} y^{15 + 6}$

Add $15$ and $6$ .

$x^{17} y^{21}$

Simplify (x^4y^3)^2*(x^3y^5)^3

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