A central mystery in high temperature superconductivity is the origin of the so-called strange metal, i.e., the anomalous conductor from which superconductivity emerges at low temperature. Measuring the dynamic charge response of the copper-oxides, $chi(q,omega)$, would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with meV resolution. Here, we present the first measurement of $chi(q,omega)$ for a cuprate, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ($T_c=91$ K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the eV energy scale. This continuum displays a simple power law form, exhibiting $q^2$ behavior at low energy and $q^2/omega^2$ behavior at high energy. Measurements of an overdoped crystal ($T_c=50$ K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled.
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