Algebra Examples

${(5 x y)}^{2} \cdot 4 x^{5}$

Step 1

Rewrite using the commutative property of multiplication.

$4 {(5 x y)}^{2} x^{5}$

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 $5 x y$ .

$4 ({(5 x)}^{2} y^{2}) x^{5}$

Step 2.2

Apply the product rule to $5 x$ .

$4 (5^{2} x^{2} y^{2}) x^{5}$

Step 3

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

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Step 3.1

Move $x^{5}$ .

$4 (5^{2} (x^{5} x^{2}) y^{2})$

Step 3.2

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

$4 (5^{2} x^{5 + 2} y^{2})$

Step 3.3

Add $5$ and $2$ .

$4 (5^{2} x^{7} y^{2})$

Step 4

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

$4 (25 x^{7} y^{2})$

Step 5

Multiply $25$ by $4$ .

$100 x^{7} y^{2}$