Pre-Algebra Examples

$- 5 w (- 6 w^{5} \cdot (9 w) - 9)$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$- 5 w (- 6 \cdot 9 w^{5} w - 9)$

Step 1.2

Multiply $w^{5}$ by $w$ by adding the exponents.

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Step 1.2.1

Move $w$ .

$- 5 w (- 6 \cdot 9 (w \cdot w^{5}) - 9)$

Step 1.2.2

Multiply $w$ by $w^{5}$ .

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Step 1.2.2.1

Raise $w$ to the power of $1$ .

$- 5 w (- 6 \cdot 9 (w^{1} w^{5}) - 9)$

Step 1.2.2.2

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

$- 5 w (- 6 \cdot 9 w^{1 + 5} - 9)$

Step 1.2.3

Add $1$ and $5$ .

$- 5 w (- 6 \cdot 9 w^{6} - 9)$

Step 1.3

Multiply $- 6$ by $9$ .

$- 5 w (- 54 w^{6} - 9)$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$- 5 w (- 54 w^{6}) - 5 w \cdot - 9$

Step 2.2

Simplify the expression.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$- 5 \cdot - 54 w \cdot w^{6} - 5 w \cdot - 9$

Step 2.2.2

Multiply $- 9$ by $- 5$ .

$- 5 \cdot - 54 w \cdot w^{6} + 45 w$

Step 3

Simplify each term.

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Step 3.1

Multiply $w$ by $w^{6}$ by adding the exponents.

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Step 3.1.1

Move $w^{6}$ .

$- 5 \cdot - 54 (w^{6} w) + 45 w$

Step 3.1.2

Multiply $w^{6}$ by $w$ .

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Step 3.1.2.1

Raise $w$ to the power of $1$ .

$- 5 \cdot - 54 (w^{6} w^{1}) + 45 w$

Step 3.1.2.2

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

$- 5 \cdot - 54 w^{6 + 1} + 45 w$

Step 3.1.3

Add $6$ and $1$ .

$- 5 \cdot - 54 w^{7} + 45 w$

Step 3.2

Multiply $- 5$ by $- 54$ .

$270 w^{7} + 45 w$