Solved on Feb 06, 2024

Evaluate the cube root of $x^{6}$ when $x=2$ .

STEP 1

Assumptions
1. We are given the expression $\sqrt[3]{x^{6}}$ .
2. We are given the value $x = 2$ .
3. We need to evaluate the expression for the given value of $x$ .

STEP 2

First, we need to understand the meaning of the cube root and the exponent in the expression. The cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is a number $b$ such that $b^3 = a$ . An exponent, such as $x^6$ , means $x$ multiplied by itself 6 times.

STEP 3

Substitute the given value of $x$ into the expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{(2)^{6}}$

STEP 4

Calculate the exponent part of the expression first. Since $x = 2$ , we raise 2 to the power of 6.
$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

STEP 5

Compute the value of $2^6$ .
$2^6 = 64$

STEP 6

Now substitute the value of $2^6$ into the cube root expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{64}$

STEP 7

Evaluate the cube root of 64. We are looking for a number that, when multiplied by itself three times, equals 64.
$\sqrt[3]{64} = 4$
Because $4 \times 4 \times 4 = 64$ .

STEP 8

The value of $\sqrt[3]{x^{6}}$ when $x = 2$ is 4.
$\sqrt[3]{x^{6}} = 4$

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Evaluate the cube root of $x^{6}$ when $x=2$ .

STEP 1

Assumptions
1. We are given the expression $\sqrt[3]{x^{6}}$ .
2. We are given the value $x = 2$ .
3. We need to evaluate the expression for the given value of $x$ .

STEP 2

First, we need to understand the meaning of the cube root and the exponent in the expression. The cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is a number $b$ such that $b^3 = a$ . An exponent, such as $x^6$ , means $x$ multiplied by itself 6 times.

STEP 3

Substitute the given value of $x$ into the expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{(2)^{6}}$

STEP 4

Calculate the exponent part of the expression first. Since $x = 2$ , we raise 2 to the power of 6.
$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

STEP 5

Compute the value of $2^6$ .
$2^6 = 64$

STEP 6

Now substitute the value of $2^6$ into the cube root expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{64}$

STEP 7

Evaluate the cube root of 64. We are looking for a number that, when multiplied by itself three times, equals 64.
$\sqrt[3]{64} = 4$
Because $4 \times 4 \times 4 = 64$ .

STEP 8

The value of $\sqrt[3]{x^{6}}$ when $x = 2$ is 4.
$\sqrt[3]{x^{6}} = 4$

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Evaluate the cube root of x6x^{6}x6 when x=2x=2x=2.

STEP 1

Assumptions1. We are given the expression x63\sqrt[3]{x^{6}}3x6​.2. We are given the value x=2x = 2x=2.3. We need to evaluate the expression for the given value of xxx.

STEP 2

First, we need to understand the meaning of the cube root and the exponent in the expression. The cube root of a number aaa, denoted as a3\sqrt[3]{a}3a​, is a number bbb such that b3=ab^3 = ab3=a. An exponent, such as x6x^6x6, means xxx multiplied by itself 6 times.

STEP 3

Substitute the given value of xxx into the expression.x63=(2)63\sqrt[3]{x^{6}} = \sqrt[3]{(2)^{6}}3x6​=3(2)6​

STEP 4

Calculate the exponent part of the expression first. Since x=2x = 2x=2, we raise 2 to the power of 6.26=2×2×2×2×2×22^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 226=2×2×2×2×2×2

STEP 5

Compute the value of 262^626.26=642^6 = 6426=64

STEP 6

Now substitute the value of 262^626 into the cube root expression.x63=643\sqrt[3]{x^{6}} = \sqrt[3]{64}3x6​=364​

STEP 7

Evaluate the cube root of 64. We are looking for a number that, when multiplied by itself three times, equals 64.643=4\sqrt[3]{64} = 4364​=4Because 4×4×4=644 \times 4 \times 4 = 644×4×4=64.

STEP 8

The value of x63\sqrt[3]{x^{6}}3x6​ when x=2x = 2x=2 is 4.x63=4\sqrt[3]{x^{6}} = 43x6​=4

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Evaluate the cube root of $x^{6}$ when $x=2$ .

Assumptions
1. We are given the expression $\sqrt[3]{x^{6}}$ .
2. We are given the value $x = 2$ .
3. We need to evaluate the expression for the given value of $x$ .

First, we need to understand the meaning of the cube root and the exponent in the expression. The cube root of a number $a$ , denoted as $\sqrt[3]{a}$ , is a number $b$ such that $b^3 = a$ . An exponent, such as $x^6$ , means $x$ multiplied by itself 6 times.

Substitute the given value of $x$ into the expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{(2)^{6}}$

Calculate the exponent part of the expression first. Since $x = 2$ , we raise 2 to the power of 6.
$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Compute the value of $2^6$ .
$2^6 = 64$

Now substitute the value of $2^6$ into the cube root expression.
$\sqrt[3]{x^{6}} = \sqrt[3]{64}$

Evaluate the cube root of 64. We are looking for a number that, when multiplied by itself three times, equals 64.
$\sqrt[3]{64} = 4$
Because $4 \times 4 \times 4 = 64$ .

The value of $\sqrt[3]{x^{6}}$ when $x = 2$ is 4.
$\sqrt[3]{x^{6}} = 4$