Question

directions: answer the questions provided. 1. write y^{-3}z^{-4} with only positive exponents. 3. simplify: (-2v^{9}) cdot (-4v^{2})

Explanation:

Step1: Apply negative - exponent rule

According to the rule $a^{-n}=\frac{1}{a^{n}}$, for $y^{-3}z^{-4}$, we can rewrite it as $\frac{1}{y^{3}}\cdot\frac{1}{z^{4}}$.

Step2: Multiply the fractions

$\frac{1}{y^{3}}\cdot\frac{1}{z^{4}}=\frac{1}{y^{3}z^{4}}$

Step1: Multiply the coefficients

Multiply - 2 and - 4. $(-2)\times(-4)=8$.

Step2: Use the product rule of exponents

According to the rule $a^{m}\cdot a^{n}=a^{m + n}$, for $v^{9}\cdot v^{2}$, we have $v^{9}\cdot v^{2}=v^{9 + 2}=v^{11}$.

Step3: Combine the results

$(-2v^{9})\cdot(-4v^{2})=8v^{11}$

Answer:

$\frac{1}{y^{3}z^{4}}$