Which two of the following numbers have a product that is between -1 and 0 ? Indicate both of the numbers. -20 -10 \( 3^{-4} \)

To determine which two numbers have a product that is between -1 and 0, we first need to evaluate the given numbers: 1. **-20** 2. **-10** 3. **\( 3^{-4} \)** Next, we calculate \( 3^{-4} \): \[ 3^{-4} = \frac{1}{3^4} = \frac{1}{81} \approx 0.0123 \] Now we have the three numbers: - -20 - -10 - \( \frac{1}{81} \) (approximately 0.0123) Next, we will check the products of the pairs of numbers: 1. **Product of -20 and -10**: \[ -20 \times -10 = 200 \] This product is not between -1 and 0. 2. **Product of -20 and \( 3^{-4} \)**: \[ -20 \times \frac{1}{81} = -\frac{20}{81} \approx -0.2469 \] This product is between -1 and 0. 3. **Product of -10 and \( 3^{-4} \)**: \[ -10 \times \frac{1}{81} = -\frac{10}{81} \approx -0.1235 \] This product is also between -1 and 0. From the calculations, the pairs that yield a product between -1 and 0 are: - **-20 and \( 3^{-4} \)** - **-10 and \( 3^{-4} \)** Thus, the two numbers that have a product between -1 and 0 are: - **-20** - **\( 3^{-4} \)** or - **-10** - **\( 3^{-4} \)** Both pairs are valid.