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Math  /  Numbers & Operations

QuestionWhat number is equal to 10×410−1×42\frac{10 \times 4}{10^{-1} \times 4^{2}} ?

Studdy Solution

STEP 1

1. We are given a mathematical expression 10×410−1×42\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 10×410 \times 4.
10×4=40 10 \times 4 = 40

STEP 4

Simplify the denominator, which is 10−1×4210^{-1} \times 4^{2}.
First, calculate 10−110^{-1}:
10−1=110 10^{-1} = \frac{1}{10}
Next, calculate 424^{2}:
42=16 4^{2} = 16
Now multiply these results:
10−1×42=110×16=1610=1.6 10^{-1} \times 4^{2} = \frac{1}{10} \times 16 = \frac{16}{10} = 1.6

STEP 5

Divide the simplified numerator by the simplified denominator.
401.6 \frac{40}{1.6}
To simplify the division, multiply both the numerator and the denominator by 1010 to eliminate the decimal:
40×101.6×10=40016 \frac{40 \times 10}{1.6 \times 10} = \frac{400}{16}
Now, perform the division:
40016=25 \frac{400}{16} = 25
The number equal to 10×410−1×42\frac{10 \times 4}{10^{-1} \times 4^{2}} is:
25\boxed{25}

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