Use the like bases property to solve the equation $$ \begin{array}{l} \left(\frac{1}{10}\right)^{x}=10000 \ x=\square \end{array} $$

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We start with the equation
$$
\left(\frac{1}{10}\right)^x = 10000.
$$
Recall that
$$
\frac{1}{10} = 10^{-1},
$$
so we can rewrite the equation as
$$
\left(10^{-1}\right)^x = 10000.
$$
Applying the power of a power rule, we have
$$
10^{-x} = 10000.
$$
Next, express $$10000$$ as a power of $$10$$. Notice that
$$
10000 = 10^4.
$$
Thus, the equation becomes
$$
10^{-x} = 10^4.
$$
Since the bases are the same, we equate the exponents:
$$
-x = 4.
$$
Finally, solve for $$x$$ by multiplying both sides by $$-1$$:
$$
x = -4.
$$
$$ x = -4 $$

Use the like bases property to solve the equation

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