Solve (ax)^(-t): Working with Negative Exponents and Multiple Variables

Solve the following equation :

$\left(a\times x\right)^{-t}=$

To solve this problem, we'll employ the following strategy:

• Step 1: Apply the power of a product rule: $\left(a \times x\right)^{-t} = a^{-t} \times x^{-t}$.
• Step 2: Apply the negative exponent rule: $a^{-t} = \frac{1}{a^t}$ and $x^{-t} = \frac{1}{x^t}$.

Here's how we do it step by step:
Step 1: We have $\left(a \times x\right)^{-t}$. By the power of a product rule, this rewrites as $a^{-t} \times x^{-t}$.
Step 2: Apply the negative exponent rule to each part:
$a^{-t} = \frac{1}{a^t}$ and $x^{-t} = \frac{1}{x^t}$.
Therefore, $a^{-t} \times x^{-t} = \frac{1}{a^t} \times \frac{1}{x^t} = \frac{1}{a^t \times x^t}$.

Thus, the solution to the equation $\left(a \times x\right)^{-t}$ is $\frac{1}{a^t \times x^t}$.