What is the value of the expression%C2%A0 (−5)−3 ? 1. Apply the negative exponent rule:%C2%A0 (−5)−3=1(−5)3 2. Expand the power:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5) 3. Simplify:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5)=1x What is the value of%C2%A0x? (1 point) Responses x=−15 x is equal to negative 15 x=125 x is equal to 125 x=15 x is equal to 15 x=−125 x is equal to negative 125

Question

What is the value of the expression%C2%A0 (−5)−3  ?  1. Apply the negative exponent rule:%C2%A0 (−5)−3=1(−5)3    2. Expand the power:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5)    3. Simplify:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5)=1x    What is the value of%C2%A0x?  (1 point) Responses  x=−15 x is equal to negative 15  x=125 x is equal to 125  x=15 x is equal to 15  x=−125 x is equal to negative 125

GPT-4o mini · Answer

To find the value of the expression $(-5)^{-3}$, we can follow the steps outlined in your question. 1. **Apply the negative exponent rule**: $$ (-5)^{-3} = \frac{1}{(-5)^3} $$ 2. **Expand the power**: $$ (-5)^{-3} = \frac{1}{(-5)^3} = \frac{1}{(-5)(-5)(-5)} $$ 3. **Simplify**: Now we need to calculate $(-5)(-5)(-5)$: - First, calculate $(-5)(-5) = 25$. - Then, calculate $25 \times (-5) = -125$. Therefore, $(-5)^3 = -125$. Putting it back into our expression: $$ (-5)^{-3} = \frac{1}{-125} = -\frac{1}{125} $$ Now we have: $$ x = -125 $$ Thus, the correct response is: - $x = -125$ (x is equal to negative 125).