Algebra Examples

${(2 x y)}^{5} \cdot 6 x^{8} y^{10}$

Step 1

Rewrite using the commutative property of multiplication.

$6 {(2 x y)}^{5} x^{8} y^{10}$

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 $2 x y$ .

$6 ({(2 x)}^{5} y^{5}) x^{8} y^{10}$

Step 2.2

Apply the product rule to $2 x$ .

$6 (2^{5} x^{5} y^{5}) x^{8} y^{10}$

Step 3

Multiply $x^{5}$ by $x^{8}$ by adding the exponents.

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Step 3.1

Move $x^{8}$ .

$6 (2^{5} (x^{8} x^{5}) y^{5}) y^{10}$

Step 3.2

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

$6 (2^{5} x^{8 + 5} y^{5}) y^{10}$

Step 3.3

Add $8$ and $5$ .

$6 (2^{5} x^{13} y^{5}) y^{10}$

Step 4

Multiply $y^{5}$ by $y^{10}$ by adding the exponents.

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Step 4.1

Move $y^{10}$ .

$6 (2^{5} x^{13} (y^{10} y^{5}))$

Step 4.2

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

$6 (2^{5} x^{13} y^{10 + 5})$

Step 4.3

Add $10$ and $5$ .

$6 (2^{5} x^{13} y^{15})$

Step 5

Raise $2$ to the power of $5$ .

$6 (32 x^{13} y^{15})$

Step 6

Multiply $32$ by $6$ .

$192 x^{13} y^{15}$