Pre-Algebra Examples

$3 y^{8} \cdot (2 y x^{- 5}) \cdot (5 v^{5} v^{- 4} x^{- 8})$

Step 1

Multiply $y^{8}$ by $y$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $y$ .

$3 (y \cdot y^{8}) \cdot (2 x^{- 5}) \cdot (5 v^{5} v^{- 4} x^{- 8})$

Step 1.2

Multiply $y$ by $y^{8}$ .

Tap for more steps...

Step 1.2.1

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

$3 (y^{1} y^{8}) \cdot (2 x^{- 5}) \cdot (5 v^{5} v^{- 4} x^{- 8})$

Step 1.2.2

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

$3 y^{1 + 8} \cdot (2 x^{- 5}) \cdot (5 v^{5} v^{- 4} x^{- 8})$

Step 1.3

Add $1$ and $8$ .

$3 y^{9} \cdot (2 x^{- 5}) \cdot (5 v^{5} v^{- 4} x^{- 8})$

Step 2

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

Tap for more steps...

Step 2.1

Move $x^{- 8}$ .

$3 y^{9} \cdot (2 (x^{- 8} x^{- 5})) \cdot (5 v^{5} v^{- 4})$

Step 2.2

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

$3 y^{9} \cdot (2 x^{- 8 - 5}) \cdot (5 v^{5} v^{- 4})$

Step 2.3

Subtract $5$ from $- 8$ .

$3 y^{9} \cdot (2 x^{- 13}) \cdot (5 v^{5} v^{- 4})$

Step 3

Multiply $v^{5}$ by $v^{- 4}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $v^{- 4}$ .

$3 y^{9} \cdot (2 x^{- 13}) \cdot (5 (v^{- 4} v^{5}))$

Step 3.2

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

$3 y^{9} \cdot (2 x^{- 13}) \cdot (5 v^{- 4 + 5})$

Step 3.3

Add $- 4$ and $5$ .

$3 y^{9} \cdot (2 x^{- 13}) \cdot (5 v^{1})$

Step 4

Simplify $3 y^{9} \cdot (2 x^{- 13}) \cdot (5 v^{1})$ .

$3 y^{9} \cdot (2 x^{- 13}) \cdot (5 v)$

Step 5

Rewrite using the commutative property of multiplication.

$3 \cdot 2 y^{9} x^{- 13} \cdot (5 v)$

Step 6

Multiply $3$ by $2$ .

$6 y^{9} x^{- 13} \cdot (5 v)$

Step 7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$6 y^{9} \frac{1}{x^{13}} \cdot (5 v)$

Step 8

Multiply $6 y^{9} \frac{1}{x^{13}}$ .

Tap for more steps...

Step 8.1

Combine $6$ and $\frac{1}{x^{13}}$ .

$y^{9} \frac{6}{x^{13}} \cdot (5 v)$

Step 8.2

Combine $y^{9}$ and $\frac{6}{x^{13}}$ .

$\frac{y^{9} \cdot 6}{x^{13}} \cdot (5 v)$

Step 9

Rewrite using the commutative property of multiplication.

$5 \frac{y^{9} \cdot 6}{x^{13}} v$

Step 10

Move $6$ to the left of $y^{9}$ .

$5 \frac{6 \cdot y^{9}}{x^{13}} v$

Step 11

Multiply $5 \frac{6 y^{9}}{x^{13}}$ .

Tap for more steps...

Step 11.1

Combine $5$ and $\frac{6 y^{9}}{x^{13}}$ .

$\frac{5 (6 y^{9})}{x^{13}} v$

Step 11.2

Multiply $6$ by $5$ .

$\frac{30 y^{9}}{x^{13}} v$

Step 12

Combine $\frac{30 y^{9}}{x^{13}}$ and $v$ .

$\frac{30 y^{9} v}{x^{13}}$