Math Snap

STEP 1

1. We are given a mathematical expression $\frac{10 \times 4}{10^{-1} \times 4^{2}}$.
2. We need to simplify this expression to find the equivalent number.

STEP 2

1. Simplify the numerator.
2. Simplify the denominator.
3. Divide the simplified numerator by the simplified denominator.

STEP 3

Simplify the numerator, which is $10 \times 4$.
$$10 \times 4 = 40$$

STEP 4

Simplify the denominator, which is $10^{-1} \times 4^{2}$.
First, calculate $10^{-1}$:
$$10^{-1} = \frac{1}{10}$$ Next, calculate $4^{2}$:
$$4^{2} = 16$$ Now multiply these results:
$$10^{-1} \times 4^{2} = \frac{1}{10} \times 16 = \frac{16}{10} = 1.6$$

Divide the simplified numerator by the simplified denominator.
$$\frac{40}{1.6}$$ To simplify the division, multiply both the numerator and the denominator by $10$ to eliminate the decimal:
$$\frac{40 \times 10}{1.6 \times 10} = \frac{400}{16}$$ Now, perform the division:
$$\frac{400}{16} = 25$$ The number equal to $\frac{10 \times 4}{10^{-1} \times 4^{2}}$ is:
$$\boxed{25}$$