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The mass of an average grain of table salt in a sample is [tex]3 \times 10^4[/tex] grams, and the mass of an average grain of rock salt in a sample is [tex]1.2 \times 10^{-2}[/tex] grams.

Part A: Using the properties of exponents, what do you need to multiply [tex]10^{-2}[/tex] by to get [tex]10^{-4}[/tex]?

Answer :

We start with the equation

$$
10^{-2} \times x = 10^{-4}.
$$

To isolate $x$, we divide both sides by $10^{-2}$:

$$
x = \frac{10^{-4}}{10^{-2}}.
$$

Using the exponent rule for division, which states that

$$
\frac{a^m}{a^n} = a^{m-n},
$$

we have

$$
x = 10^{-4 - (-2)} = 10^{-4+2} = 10^{-2}.
$$

Thus, you need to multiply $10^{-2}$ by $10^{-2}$ to obtain $10^{-4}$.

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