Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 19, 2024

Solve for $m$ in the equation $-64=m^{3}$ . Express the solution in simplest radical form.

STEP 1

Assumptions
1. We are given the equation $-64 = m^{3}$ .
2. We need to solve for $m$ .
3. The solution should be expressed in simplest radical form if necessary.

STEP 2

To solve for $m$ , we need to take the cube root of both sides of the equation to isolate $m$ .
$m = \sqrt[3]{-64}$

STEP 3

We recognize that $-64$ is a perfect cube, as $-4 \times -4 \times -4 = -64$ .

STEP 4

Take the cube root of $-64$ .
$m = \sqrt[3]{-64} = -4$

STEP 5

We have found the value of $m$ .
$m = -4$
This is already in the simplest form, and no radical form is necessary because the cube root of a perfect cube is an integer.
The solution for $m$ is $-4$ .

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