Algebra Examples

$- 3 {(2 x)}^{4} {(4 x^{5} y)}^{2}$

Step 1

Apply the product rule to $2 x$ .

$- 3 (2^{4} x^{4}) {(4 x^{5} y)}^{2}$

Step 2

Raise $2$ to the power of $4$ .

$- 3 (16 x^{4}) {(4 x^{5} y)}^{2}$

Step 3

Multiply $16$ by $- 3$ .

$- 48 x^{4} {(4 x^{5} y)}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $4 x^{5} y$ .

$- 48 x^{4} ({(4 x^{5})}^{2} y^{2})$

Step 4.2

Apply the product rule to $4 x^{5}$ .

$- 48 x^{4} (4^{2} {(x^{5})}^{2} y^{2})$

Step 5

Raise $4$ to the power of $2$ .

$- 48 x^{4} (16 {(x^{5})}^{2} y^{2})$

Step 6

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 6.1

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

$- 48 x^{4} (16 x^{5 \cdot 2} y^{2})$

Step 6.2

Multiply $5$ by $2$ .

$- 48 x^{4} (16 x^{10} y^{2})$

Step 7

Multiply $x^{4}$ by $x^{10}$ by adding the exponents.

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Step 7.1

Move $x^{10}$ .

$- 48 (x^{10} x^{4}) (16 y^{2})$

Step 7.2

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

$- 48 x^{10 + 4} (16 y^{2})$

Step 7.3

Add $10$ and $4$ .

$- 48 x^{14} (16 y^{2})$

Step 8

Rewrite using the commutative property of multiplication.

$- 48 \cdot 16 x^{14} y^{2}$

Step 9

Multiply $- 48$ by $16$ .

$- 768 x^{14} y^{2}$