QuestionOpen with $-=$ 4.

Studdy Solution

STEP 1

1. We are given two expressions: the cube root of $-216$ and the fraction with the square root of $144$ in the numerator and $-2$ in the denominator.
2. We need to simplify both expressions separately.
3. We need to compare the simplified results using the appropriate comparison symbol.

STEP 2

1. Simplify the cube root of $-216$ .
2. Simplify the fraction with the square root of $144$ in the numerator and $-2$ in the denominator.
3. Compare the two simplified results.

STEP 3

Simplify the cube root of $-216$ .
$\sqrt[3]{-216} = -\sqrt[3]{216}$

STEP 4

Calculate the cube root of $216$ .
$\sqrt[3]{216} = 6$

STEP 5

Thus, the cube root of $-216$ simplifies to:
$\sqrt[3]{-216} = -6$

STEP 6

Simplify the fraction with the square root of $144$ in the numerator and $-2$ in the denominator.
$\frac{\sqrt{144}}{-2}$

STEP 7

Calculate the square root of $144$ .
$\sqrt{144} = 12$

STEP 8

Thus, the fraction simplifies to:
$\frac{12}{-2} = -6$

STEP 9

Compare the two simplified results:
$-6 \quad \text{and} \quad -6$

STEP 10

Since both values are equal, the correct comparison symbol is:
$-6 \quad = \quad -6$
Conclusion: The cube root of $-216$ is equal to the fraction with the square root of $144$ in the numerator and $-2$ in the denominator.
$\sqrt[3]{-216} = \frac{\sqrt{144}}{-2}$

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