Questions: Choose the answer that uses positive exponents to correctly simplify this expression. [ left[left(-2 a^-2 b^-3right)^2right]^0 ] A B C 1/2 1

Solution Steps

The given expression is: \[ \left[\left(-2 a^{-2} b^{-3}\right)^{2}\right]^{0} \]

First, simplify the inner expression \(\left(-2 a^{-2} b^{-3}\right)^{2}\). Recall that when you raise a product to a power, you raise each factor to that power: \[ \left(-2 a^{-2} b^{-3}\right)^{2} = (-2)^{2} \cdot (a^{-2})^{2} \cdot (b^{-3})^{2} \]

Calculate each part: \[ (-2)^{2} = 4 \] \[ (a^{-2})^{2} = a^{-4} \] \[ (b^{-3})^{2} = b^{-6} \]

So, the inner expression simplifies to: \[ 4 a^{-4} b^{-6} \]

Now, raise the simplified expression to the power of 0: \[ \left(4 a^{-4} b^{-6}\right)^{0} \]

Recall that any non-zero number raised to the power of 0 is 1: \[ \left(4 a^{-4} b^{-6}\right)^{0} = 1 \]

Final Answer