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Solve for x: x⁻⁴ = 16.

May 17, 2026Mathematics

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Step-by-step solution

3 steps

Identify the given equation.
The visible part of the equation is $...^{-4} = 16$ . Let the unknown base be $x$ .
So, the equation is $x^{-4} = 16$ .
Rewrite the exponent using the property $(a^m)^n = a^{mn}$ .
We can write $x^{-4}$ as $(x^{-2})^2$ .
Substituting this into the equation gives:
$(x^{-2})^2 = 16$
Solve for $x^{-2}$ by taking the square root of both sides.
$\sqrt{(x^{-2})^2} = \pm \sqrt{16}$ $x^{-2} = \pm 4$

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