3x= (-64)⅓ solve this indices.

October 12, 2026Mathematics

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Answer

x = -\frac{4}{3}

4 steps

Here's the solution:

Evaluate the right-hand side of the equation.
The exponent $\frac{1}{3}$ represents the cube root.
$(-64)^{\frac{1}{3}} = \sqrt[3]{-64}$
Calculate the cube root of $-64$ .
We need a number that, when multiplied by itself three times, equals $-64$ .
$(-4) \times (-4) \times (-4) = 16 \times (-4) = -64$
So, $\sqrt[3]{-64} = -4$ .
Substitute this value back into the original equation.
$3x = -4$
Solve for $x$ .
Divide both sides by 3.
$x = \frac{-4}{3}$
The solution is $x = -\frac{4}{3}$ .

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