Algebra Examples

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

Step 1

Apply the product rule to $3 y$ .

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

Raise $3$ to the power of $2$ .

${(6 \cdot 9 x y^{2})}^{2}$

Step 4

Multiply $6$ by $9$ .

${(54 x y^{2})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $54 x y^{2}$ .

${(54 x)}^{2} {(y^{2})}^{2}$

Step 5.2

Apply the product rule to $54 x$ .

$54^{2} x^{2} {(y^{2})}^{2}$

Step 6

Raise $54$ to the power of $2$ .

$2916 x^{2} {(y^{2})}^{2}$

Step 7

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

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Step 7.1

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

$2916 x^{2} y^{2 \cdot 2}$

Step 7.2

Multiply $2$ by $2$ .

$2916 x^{2} y^{4}$