Basic Math Examples

${(9 b^{2})}^{2} {(a^{2} b^{4})}^{3}$

Step 1

Apply the product rule to $9 b^{2}$ .

$9^{2} {(b^{2})}^{2} {(a^{2} b^{4})}^{3}$

Step 2

Raise $9$ to the power of $2$ .

$81 {(b^{2})}^{2} {(a^{2} b^{4})}^{3}$

Step 3

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

Tap for more steps...

Step 3.1

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

$81 b^{2 \cdot 2} {(a^{2} b^{4})}^{3}$

Step 3.2

Multiply $2$ by $2$ .

$81 b^{4} {(a^{2} b^{4})}^{3}$

Step 4

Apply the product rule to $a^{2} b^{4}$ .

$81 b^{4} ({(a^{2})}^{3} {(b^{4})}^{3})$

Step 5

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

Tap for more steps...

Step 5.1

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

$81 b^{4} (a^{2 \cdot 3} {(b^{4})}^{3})$

Step 5.2

Multiply $2$ by $3$ .

$81 b^{4} (a^{6} {(b^{4})}^{3})$

Step 6

Multiply the exponents in ${(b^{4})}^{3}$ .

Tap for more steps...

Step 6.1

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

$81 b^{4} (a^{6} b^{4 \cdot 3})$

Step 6.2

Multiply $4$ by $3$ .

$81 b^{4} (a^{6} b^{12})$

Step 7

Multiply $b^{4}$ by $b^{12}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $b^{12}$ .

$81 (b^{12} b^{4}) a^{6}$

Step 7.2

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

$81 b^{12 + 4} a^{6}$

Step 7.3

Add $12$ and $4$ .

$81 b^{16} a^{6}$