Final answer:
The expression 43(−2^10) does not involve the zero power rule and simplifies to 44032. If −2^0 was intended, by the zero power rule the expression would simplify to 43, corresponding to option (a) 43. However, with the original expression, none of the given options apply.
Step-by-step explanation:
The question here involves applying the zero power rule to simplify the expression 43(−2^10). The zero power rule states that any nonzero number raised to the power of zero is equal to one (e.g., a^0 = 1 for a ≠ 0). This rule is not directly applicable to the given expression as there isn't an exponent of zero present. Instead, this appears to be a multiplication problem involving an exponent.
To simplify the expression, we do not change the coefficient 43, but instead focus on simplifying the power of −2. The expression −2^10 means −2 is multiplied by itself 10 times. Computing this, we get:
- (−2) x (−2) x (−2) x (−2) x (−2) x (−2) x (−2) x (−2) x (−2) x (−2) = 1024
- 43 x 1024 = 44032
However, the options given all represent division, suggesting there might be a misunderstanding in the question. If the expression were indeed 43(−2^0), then applying the zero power rule would result in:
- (−2^0) = 1 (since any number to the zero power equals one)
- 43 x 1 = 43
Therefore, assuming that −2^0 was intended, the equivalent expression would be simplified to 43, which would correspond to option (a) 43.
However, with the original question as stated, none of the given options are correct since 43(−2^10) does not simplify to a form involving division by a power of two.