Solved on Mar 06, 2024

Find the value of $c$ , where $c = \sqrt[3]{-20}^3$ .

STEP 1

Assumptions
1. We are asked to simplify the expression for $c$ .
2. The expression involves cube roots of negative numbers.
3. The cube root of a negative number is a negative number.

STEP 2

First, we recognize that the cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is the number which, when multiplied by itself three times, gives the number $a$ .

STEP 3

We can use the property of exponents that states $(\sqrt[3]{a})^3 = a$ . This means that if we multiply the cube root of a number by itself three times, we get the original number.

STEP 4

Now, let's apply this property to the given expression, $c = \sqrt[3]{-20} \cdot \sqrt[3]{-20} \cdot \sqrt[3]{-20}$ .

STEP 5

We can rewrite the expression as a single cube root raised to the third power.
$c = (\sqrt[3]{-20})^3$

STEP 6

Now, we can simplify the expression by recognizing that raising a cube root to the third power will give us the radicand (the number under the cube root).
$c = -20$

STEP 7

The simplified expression for $c$ is just the radicand itself, which is $-20$ .
The solution for $c$ is $-20$ .

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Find the value of $c$ , where $c = \sqrt[3]{-20}^3$ .

STEP 1

Assumptions
1. We are asked to simplify the expression for $c$ .
2. The expression involves cube roots of negative numbers.
3. The cube root of a negative number is a negative number.

STEP 2

First, we recognize that the cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is the number which, when multiplied by itself three times, gives the number $a$ .

STEP 3

We can use the property of exponents that states $(\sqrt[3]{a})^3 = a$ . This means that if we multiply the cube root of a number by itself three times, we get the original number.

STEP 4

Now, let's apply this property to the given expression, $c = \sqrt[3]{-20} \cdot \sqrt[3]{-20} \cdot \sqrt[3]{-20}$ .

STEP 5

We can rewrite the expression as a single cube root raised to the third power.
$c = (\sqrt[3]{-20})^3$

STEP 6

Now, we can simplify the expression by recognizing that raising a cube root to the third power will give us the radicand (the number under the cube root).
$c = -20$

STEP 7

The simplified expression for $c$ is just the radicand itself, which is $-20$ .
The solution for $c$ is $-20$ .

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Find the value of ccc, where c=−2033c = \sqrt[3]{-20}^3c=3−20​3.

STEP 1

Assumptions1. We are asked to simplify the expression for ccc.2. The expression involves cube roots of negative numbers.3. The cube root of a negative number is a negative number.

STEP 2

First, we recognize that the cube root of a number aaa, denoted as a3\sqrt[3]{a}3a​, is the number which, when multiplied by itself three times, gives the number aaa.

STEP 3

We can use the property of exponents that states (a3)3=a(\sqrt[3]{a})^3 = a(3a​)3=a. This means that if we multiply the cube root of a number by itself three times, we get the original number.

STEP 4

Now, let's apply this property to the given expression, c=−203⋅−203⋅−203c = \sqrt[3]{-20} \cdot \sqrt[3]{-20} \cdot \sqrt[3]{-20}c=3−20​⋅3−20​⋅3−20​.

STEP 5

We can rewrite the expression as a single cube root raised to the third power.c=(−203)3c = (\sqrt[3]{-20})^3c=(3−20​)3

STEP 6

Now, we can simplify the expression by recognizing that raising a cube root to the third power will give us the radicand (the number under the cube root).c=−20c = -20c=−20

STEP 7

The simplified expression for ccc is just the radicand itself, which is −20-20−20.The solution for ccc is −20-20−20.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $c$ , where $c = \sqrt[3]{-20}^3$ .

Assumptions
1. We are asked to simplify the expression for $c$ .
2. The expression involves cube roots of negative numbers.
3. The cube root of a negative number is a negative number.

First, we recognize that the cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is the number which, when multiplied by itself three times, gives the number $a$ .

We can use the property of exponents that states $(\sqrt[3]{a})^3 = a$ . This means that if we multiply the cube root of a number by itself three times, we get the original number.

Now, let's apply this property to the given expression, $c = \sqrt[3]{-20} \cdot \sqrt[3]{-20} \cdot \sqrt[3]{-20}$ .

We can rewrite the expression as a single cube root raised to the third power.
$c = (\sqrt[3]{-20})^3$

Now, we can simplify the expression by recognizing that raising a cube root to the third power will give us the radicand (the number under the cube root).
$c = -20$

The simplified expression for $c$ is just the radicand itself, which is $-20$ .
The solution for $c$ is $-20$ .