Question

calculate
$\left(-2.00 \times 10^{-4}\
ight)^{-3}$
write your answer in scientific notation.

Explanation:

Step1: Apply exponent rule to base

Recall that $(ab)^n = a^n b^n$ and $a^{-n}=\frac{1}{a^n}$.
$$(-2.00 \times 10^{-4})^{-3} = \frac{1}{(-2.00 \times 10^{-4})^{3}}$$

Step2: Expand the denominator

Calculate each term's cube.
$$\frac{1}{(-2.00)^3 \times (10^{-4})^3} = \frac{1}{-8.00 \times 10^{-12}}$$

Step3: Simplify the fraction

Rewrite as a negative coefficient and adjust exponent.
$$- \frac{1}{8.00} \times 10^{12} = -0.125 \times 10^{12}$$

Step4: Convert to scientific notation

Adjust coefficient to $1 \leq |a| < 10$.
$$-1.25 \times 10^{11}$$

Answer:

$-1.25 \times 10^{11}$