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

Answer 1

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).