Basic Math Examples

${(3 a^{2} y^{3})}^{3} (2 a^{3} y^{4} z)$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(3 a^{2} y^{3})}^{3} a^{3} y^{4} z$

Step 2

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

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Step 2.1

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

$2 ({(3 a^{2})}^{3} {(y^{3})}^{3}) a^{3} y^{4} z$

Step 2.2

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

$2 (3^{3} {(a^{2})}^{3} {(y^{3})}^{3}) a^{3} y^{4} z$

Step 3

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

$2 (27 {(a^{2})}^{3} {(y^{3})}^{3}) a^{3} y^{4} z$

Step 4

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

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Step 4.1

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

$2 (27 a^{2 \cdot 3} {(y^{3})}^{3}) a^{3} y^{4} z$

Step 4.2

Multiply $2$ by $3$ .

$2 (27 a^{6} {(y^{3})}^{3}) a^{3} y^{4} z$

Step 5

Multiply $a^{6}$ by $a^{3}$ by adding the exponents.

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Step 5.1

Move $a^{3}$ .

$2 (27 (a^{3} a^{6}) {(y^{3})}^{3}) y^{4} z$

Step 5.2

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

$2 (27 a^{3 + 6} {(y^{3})}^{3}) y^{4} z$

Step 5.3

Add $3$ and $6$ .

$2 (27 a^{9} {(y^{3})}^{3}) y^{4} z$

Step 6

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

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Step 6.1

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

$2 (27 a^{9} y^{3 \cdot 3}) y^{4} z$

Step 6.2

Multiply $3$ by $3$ .

$2 (27 a^{9} y^{9}) y^{4} z$

Step 7

Multiply $y^{9}$ by $y^{4}$ by adding the exponents.

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Step 7.1

Move $y^{4}$ .

$2 (27 a^{9} (y^{4} y^{9})) z$

Step 7.2

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

$2 (27 a^{9} y^{4 + 9}) z$

Step 7.3

Add $4$ and $9$ .

$2 (27 a^{9} y^{13}) z$

Step 8

Multiply $27$ by $2$ .

$54 a^{9} y^{13} z$