which of these expressions represents the expanded form of the following exponent?\n$10^{-4}$\nshow your…

which of these expressions represents the expanded form of the following exponent?\n$10^{-4}$\nshow your work here\n$\bigcirc$ $10 cdot -4$\n$\bigcirc$ $10 cdot 10 cdot 10 cdot 10$\n$\bigcirc$ $\frac{1}{10} cdot \frac{1}{10} cdot \frac{1}{10} cdot \frac{1}{10}$\n$\bigcirc$ $-4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4$

which of these expressions represents the expanded form of the following exponent?\n$10^{-4}$\nshow your work here\n$\bigcirc$ $10 cdot -4$\n$\bigcirc$ $10 cdot 10 cdot 10 cdot 10$\n$\bigcirc$ $\frac{1}{10} cdot \frac{1}{10} cdot \frac{1}{10} cdot \frac{1}{10}$\n$\bigcirc$ $-4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4 cdot -4$

Answer

Explanation:

Step1: Recall negative exponent rule

For any non-zero number $a$ and positive integer $n$, $a^{-n} = \frac{1}{a^n}$ So $10^{-4} = \frac{1}{10^4}$

Step2: Expand positive exponent

$10^4$ means $10 \cdot 10 \cdot 10 \cdot 10$, so $\frac{1}{10^4} = \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}$

Answer:

$\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}$ (the third option)