Algebra Examples

${(2 a^{3} b^{2})}^{0} {(3 a^{2})}^{2}$

Step 1

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

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Step 1.1

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

${(2 a^{3})}^{0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 1.2

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

$2^{0} {(a^{3})}^{0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 2

Anything raised to $0$ is $1$ .

$1 {(a^{3})}^{0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 3

Multiply ${(a^{3})}^{0}$ by $1$ .

${(a^{3})}^{0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 4

Multiply the exponents in ${(a^{3})}^{0}$ .

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Step 4.1

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

$a^{3 \cdot 0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 4.2

Multiply $3$ by $0$ .

$a^{0} {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 5

Anything raised to $0$ is $1$ .

$1 {(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 6

Multiply ${(b^{2})}^{0}$ by $1$ .

${(b^{2})}^{0} {(3 a^{2})}^{2}$

Step 7

Multiply the exponents in ${(b^{2})}^{0}$ .

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Step 7.1

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

$b^{2 \cdot 0} {(3 a^{2})}^{2}$

Step 7.2

Multiply $2$ by $0$ .

$b^{0} {(3 a^{2})}^{2}$

Step 8

Anything raised to $0$ is $1$ .

$1 {(3 a^{2})}^{2}$

Step 9

Multiply ${(3 a^{2})}^{2}$ by $1$ .

${(3 a^{2})}^{2}$

Step 10

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

$3^{2} {(a^{2})}^{2}$

Step 11

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

$9 {(a^{2})}^{2}$

Step 12

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

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Step 12.1

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

$9 a^{2 \cdot 2}$

Step 12.2

Multiply $2$ by $2$ .

$9 a^{4}$