Question

simplify.

\\2v^{-3} \cdot 3u^9 u^{-9} x^2 x \cdot 4v^{-7}\\

use only positive exponents in your answer.

Explanation:

Group the coefficients and variables

Using the Algebraic Simplification knowledge point

$$ 2v^{-3} \cdot 3u^9 u^{-9} x^2 x \cdot 4v^{-7} = (2 \cdot 3 \cdot 4) \cdot (u^9 \cdot u^{-9}) \cdot (x^2 \cdot x) \cdot (v^{-3} \cdot v^{-7}) $$

Multiply the numerical coefficients

Using the Algebraic Simplification knowledge point

$$ 2 \cdot 3 \cdot 4 = 24 $$

Simplify the variable bases using exponent rules

Using the Algebraic Simplification knowledge point

$$
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$$

Combine the simplified terms

Using the Algebraic Simplification knowledge point

$$ 24 \cdot 1 \cdot x^3 \cdot v^{-10} = 24x^3v^{-10} $$

Convert to positive exponents

Using the Negative Exponents knowledge point

$$ 24x^3v^{-10} = \frac{24x^3}{v^{10}} $$

Answer:

$$\frac{24x^3}{v^{10}}$$