By what number should `(-4)^(2)` be multiplied so that the product may be equal to `10^(-2)`?

Answer

To solve the problem step by step, we need to find the number \( y \) such that:

\[ (-4)^2 \times y = 10^{-2} \]

### Step 1: Calculate \( (-4)^2 \)

First, we calculate \( (-4)^2 \):

\[ (-4)^2 = (-4) \times (-4) = 16 \]

### Step 2: Set up the equation

Now we can substitute this value into the equation:

\[ 16 \times y = 10^{-2} \]

### Step 3: Isolate \( y \)

To find \( y \), we need to isolate it. We can do this by dividing both sides of the equation by 16:

\[ y = \frac{10^{-2}}{16} \]

### Step 4: Rewrite \( 10^{-2} \)

Next, we can rewrite \( 10^{-2} \) using the property of exponents:

\[ 10^{-2} = \frac{1}{10^2} = \frac{1}{100} \]

### Step 5: Substitute back into the equation

Now we substitute this back into our equation for \( y \):

\[ y = \frac{1/100}{16} \]

### Step 6: Simplify the fraction

To simplify \( y \), we can multiply the fractions:

\[ y = \frac{1}{100 \times 16} = \frac{1}{1600} \]

### Conclusion

Thus, the number that should be multiplied by \( (-4)^2 \) to get \( 10^{-2} \) is:

\[ y = \frac{1}{1600} \]

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