Pre-Algebra Examples

$v^{- 1 \div 7 v^{- 3}} \cdot (4 v^{2})$

Step 1

Rewrite using the commutative property of multiplication.

$4 v^{- 1 \div 7 v^{- 3}} v^{2}$

Step 2

Multiply $v^{- 1 \div 7 v^{- 3}}$ by $v^{2}$ by adding the exponents.

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Step 2.1

Move $v^{2}$ .

$4 (v^{2} v^{- 1 \div 7 v^{- 3}})$

Step 2.2

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

$4 v^{2 + - 1 \div 7 v^{- 3}}$

Step 2.3

Simplify each term.

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Step 2.3.1

Rewrite the division as a fraction.

$4 v^{2 + \frac{- 1}{7 v^{- 3}}}$

Step 2.3.2

Move $v^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 v^{2 + \frac{- v^{3}}{7}}$

Step 2.3.3

Move the negative in front of the fraction.

$4 v^{2 - \frac{v^{3}}{7}}$