Questions: Choose the answer that uses positive exponents to correctly simplify this expression. [ left(-2 a^-2right)^3left(-5 a^-3right)^2 ] A frac-200a^6 - B frac200a^12 frac-200a^12

$Choose the answer that uses positive exponents to correctly simplify this expression. [ left(-2 a^-2right)^3left(-5 a^-3right)^2 ] A frac-200a^6 - B frac200a^12 frac-200a^12$

Transcript text: Choose the answer that uses positive exponents to correctly simplify this expression. \[ \left(-2 a^{-2}\right)^{3}\left(-5 a^{-3}\right)^{2} \] \[ \begin{array}{ccc} A \\ \frac{-200}{a^{6}} & - & \text { B } \\ \frac{200}{a^{12}} & \frac{-200}{a^{12}} \end{array} \]

Solution

Solution Steps

Step 1: Simplify the first part of the expression

The first part of the expression is $\left(-2 a^{-2}\right)^{3}$. We can simplify this as follows: \[ \left(-2 a^{-2}\right)^{3} = (-2)^{3} \cdot \left(a^{-2}\right)^{3} = -8 \cdot a^{-6} \]

Step 2: Simplify the second part of the expression

The second part of the expression is $\left(-5 a^{-3}\right)^{2}$. We can simplify this as follows: \[ \left(-5 a^{-3}\right)^{2} = (-5)^{2} \cdot \left(a^{-3}\right)^{2} = 25 \cdot a^{-6} \]

Step 3: Multiply the simplified parts together

Now, multiply the simplified parts from Step 1 and Step 2: \[ -8 \cdot a^{-6} \cdot 25 \cdot a^{-6} = -200 \cdot a^{-12} \]

Step 4: Rewrite the expression using positive exponents

To express the final answer with positive exponents, we rewrite $a^{-12}$ as $\frac{1}{a^{12}}$: \[ -200 \cdot a^{-12} = \frac{-200}{a^{12}} \]