Final answer:
The expressions (-3)-5 equals 1/(-3)5, which is 1/-243. This value is negative and less than 1. The true statements about (-3)-5 are (E) . (−3)⁻⁵ is less than 1 and (F) Negative 3 to the negative 5 power is less than 1.
Step-by-step explanation:
The student is asking about the properties of the number (-3)-5. To evaluate this expression, we need to understand the rules of exponents and how they relate to negative bases and negative exponents.
The key is to recognize that a negative exponent indicates an inverse, so (-3)-5 is the same as 1/(-3)5.
First, let's consider the magnitude without the negative sign: 35 equals 3 × 3 × 3 × 3 × 3, which is 243.
Translating this back to our original expression with a negative base and negative exponent, 1/(-3)5 is equivalent to 1/-243.
This means that the result will be negative, and since -1/243 is less than 1 in absolute value, the statement that (-3)-5 is less than 1 is true (E and F).
However, none of the other provided statements (A, B, C, D, G) are true, as (-3)-5 does not equal -15, -243, or -1243. Therefore, the correct answers that should be selected are E and F.