Compare 7.6 × 10 to the power of −25 and 6.7 × 10 to the power of −52 . Which statement is true?(1 point)

Question

Compare  7.6 × 10 to the power of −25  and  6.7 × 10 to the power of −52 . Which statement is true?(1 point)
Responses

7.6 × 10 to the power of −25 > 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 < 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 = 6.7 × 10 to the power of −52
7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline

7.6 × 10 to the power of −25 ≤ 6.7 × 10 to the power of −52

GPT-4o mini · Answer

To compare $ 7.6 \times 10^{-25} $ and $ 6.7 \times 10^{-52} $, we can compare their values by first noting the exponent of 10. 1. The first number is $ 7.6 \times 10^{-25} $. 2. The second number is $ 6.7 \times 10^{-52} $. Since both numbers are in scientific notation, we can analyze their exponents: - The exponent $-25$ is greater than $-52$. This means that $ 10^{-25} $ is significantly larger than $ 10^{-52} $. Now let's compare combining the coefficients: - $7.6 \times 10^{-25}$ can be thought of as $7.6$ multiplied by a larger number compared to $6.7 \times 10^{-52}$, which is effectively $6.7$ multiplied by a much smaller number. Thus, $ 7.6 \times 10^{-25} $ is indeed greater than $ 6.7 \times 10^{-52} $. The true statement is: **7.6 × 10 to the power of −25 > 6.7 × 10 to the power of −52**.