Question Evaluate the expression $(-3)^{3}$ .

Studdy Solution

STEP 1

Assumptions
1. We are calculating the cube of a negative number, which is $(-3)^3$ .
2. The cube of a number $a$ is given by $a^3 = a \times a \times a$ .

STEP 2

We will use the definition of exponentiation to calculate the cube of $-3$ .
$(-3)^3 = (-3) \times (-3) \times (-3)$

STEP 3

First, calculate the product of the first two factors.
$(-3) \times (-3) = 9$

STEP 4

Now, multiply the result from STEP_3 by the third factor.
$9 \times (-3)$

STEP 5

Calculate the final product.
$9 \times (-3) = -27$
The result of $(-3)^{3}$ is $-27$ .

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Question Evaluate the expression $(-3)^{3}$ .

Studdy Solution

STEP 1

Assumptions
1. We are calculating the cube of a negative number, which is $(-3)^3$ .
2. The cube of a number $a$ is given by $a^3 = a \times a \times a$ .

STEP 2

We will use the definition of exponentiation to calculate the cube of $-3$ .
$(-3)^3 = (-3) \times (-3) \times (-3)$

STEP 3

First, calculate the product of the first two factors.
$(-3) \times (-3) = 9$

STEP 4

Now, multiply the result from STEP_3 by the third factor.
$9 \times (-3)$

STEP 5

Calculate the final product.
$9 \times (-3) = -27$
The result of $(-3)^{3}$ is $-27$ .

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Question Evaluate the expression (−3)3(-3)^{3}(−3)3.

Studdy Solution

STEP 1

Assumptions1. We are calculating the cube of a negative number, which is (−3)3(-3)^3(−3)3.2. The cube of a number aaa is given by a3=a×a×aa^3 = a \times a \times aa3=a×a×a.

STEP 2

We will use the definition of exponentiation to calculate the cube of −3-3−3.(−3)3=(−3)×(−3)×(−3)(-3)^3 = (-3) \times (-3) \times (-3)(−3)3=(−3)×(−3)×(−3)

STEP 3

First, calculate the product of the first two factors.(−3)×(−3)=9(-3) \times (-3) = 9(−3)×(−3)=9

STEP 4

Now, multiply the result from STEP_3 by the third factor.9×(−3)9 \times (-3)9×(−3)

STEP 5

Calculate the final product.9×(−3)=−279 \times (-3) = -279×(−3)=−27The result of (−3)3(-3)^{3}(−3)3 is −27-27−27.

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Question Evaluate the expression $(-3)^{3}$ .

Assumptions
1. We are calculating the cube of a negative number, which is $(-3)^3$ .
2. The cube of a number $a$ is given by $a^3 = a \times a \times a$ .

We will use the definition of exponentiation to calculate the cube of $-3$ .
$(-3)^3 = (-3) \times (-3) \times (-3)$

First, calculate the product of the first two factors.
$(-3) \times (-3) = 9$

Now, multiply the result from STEP_3 by the third factor.
$9 \times (-3)$

Calculate the final product.
$9 \times (-3) = -27$
The result of $(-3)^{3}$ is $-27$ .