Solved on Jan 18, 2024

Rewrite the expression $x^{\frac{9}{7}}$ . Select the correct answer: A. $\left(\frac{1}{\sqrt{x}}\right)^{9}$ , B. $x \sqrt[7]{x^{2}}$ , C. $\sqrt[9]{x^{7}}$ , D. $x \sqrt[7]{x}$ .

STEP 1

Assumptions
1. We need to rewrite the expression $x^{\frac{9}{7}}$ in a different form.
2. We are given multiple choice answers and must select the correct one.

STEP 2

Understand the exponentiation rules that can be used to rewrite the expression. The expression $x^{\frac{9}{7}}$ can be rewritten using the rule $x^{\frac{a}{b}} = \sqrt[b]{x^{a}}$ , where $a$ and $b$ are integers.

STEP 3

Apply the exponentiation rule to the given expression.
$x^{\frac{9}{7}} = \sqrt[7]{x^{9}}$

STEP 4

Now, we need to simplify $\sqrt[7]{x^{9}}$ if possible. We can rewrite $x^{9}$ as $x^{7} \cdot x^{2}$ because $9 = 7 + 2$ .

STEP 5

Substitute $x^{9}$ with $x^{7} \cdot x^{2}$ in the radical expression.
$\sqrt[7]{x^{9}} = \sqrt[7]{x^{7} \cdot x^{2}}$

STEP 6

According to the properties of radicals, $\sqrt[7]{x^{7} \cdot x^{2}}$ can be split into the product of two radicals: $\sqrt[7]{x^{7}} \cdot \sqrt[7]{x^{2}}$ .

STEP 7

Simplify the first radical. Since the index of the radical and the exponent are the same, $\sqrt[7]{x^{7}} = x$ .

STEP 8

Combine the simplified radicals.
$\sqrt[7]{x^{7} \cdot x^{2}} = x \cdot \sqrt[7]{x^{2}}$

STEP 9

Now, we compare the expression we have obtained with the given options.

STEP 10

We see that $x \cdot \sqrt[7]{x^{2}}$ matches option B.
$x \cdot \sqrt[7]{x^{2}} = x \sqrt[7]{x^{2}}$

STEP 11

Select the correct answer based on the comparison.
The correct answer is B. $x \sqrt[7]{x^{2}}$ .

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Rewrite the expression $x^{\frac{9}{7}}$ . Select the correct answer: A. $\left(\frac{1}{\sqrt{x}}\right)^{9}$ , B. $x \sqrt[7]{x^{2}}$ , C. $\sqrt[9]{x^{7}}$ , D. $x \sqrt[7]{x}$ .

STEP 1

Assumptions
1. We need to rewrite the expression $x^{\frac{9}{7}}$ in a different form.
2. We are given multiple choice answers and must select the correct one.

STEP 2

Understand the exponentiation rules that can be used to rewrite the expression. The expression $x^{\frac{9}{7}}$ can be rewritten using the rule $x^{\frac{a}{b}} = \sqrt[b]{x^{a}}$ , where $a$ and $b$ are integers.

STEP 3

Apply the exponentiation rule to the given expression.
$x^{\frac{9}{7}} = \sqrt[7]{x^{9}}$

STEP 4

Now, we need to simplify $\sqrt[7]{x^{9}}$ if possible. We can rewrite $x^{9}$ as $x^{7} \cdot x^{2}$ because $9 = 7 + 2$ .

STEP 5

Substitute $x^{9}$ with $x^{7} \cdot x^{2}$ in the radical expression.
$\sqrt[7]{x^{9}} = \sqrt[7]{x^{7} \cdot x^{2}}$

STEP 6

According to the properties of radicals, $\sqrt[7]{x^{7} \cdot x^{2}}$ can be split into the product of two radicals: $\sqrt[7]{x^{7}} \cdot \sqrt[7]{x^{2}}$ .

STEP 7

Simplify the first radical. Since the index of the radical and the exponent are the same, $\sqrt[7]{x^{7}} = x$ .

STEP 8

Combine the simplified radicals.
$\sqrt[7]{x^{7} \cdot x^{2}} = x \cdot \sqrt[7]{x^{2}}$

STEP 9

Now, we compare the expression we have obtained with the given options.

STEP 10

We see that $x \cdot \sqrt[7]{x^{2}}$ matches option B.
$x \cdot \sqrt[7]{x^{2}} = x \sqrt[7]{x^{2}}$

STEP 11

Select the correct answer based on the comparison.
The correct answer is B. $x \sqrt[7]{x^{2}}$ .

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Rewrite the expression x97x^{\frac{9}{7}}x79​. Select the correct answer: A. (1x)9\left(\frac{1}{\sqrt{x}}\right)^{9}(x​1​)9, B. xx27x \sqrt[7]{x^{2}}x7x2​, C. x79\sqrt[9]{x^{7}}9x7​, D. xx7x \sqrt[7]{x}x7x​.

STEP 1

Assumptions1. We need to rewrite the expression x97x^{\frac{9}{7}}x79​ in a different form.2. We are given multiple choice answers and must select the correct one.

STEP 2

Understand the exponentiation rules that can be used to rewrite the expression. The expression x97x^{\frac{9}{7}}x79​ can be rewritten using the rule xab=xabx^{\frac{a}{b}} = \sqrt[b]{x^{a}}xba​=bxa​, where aaa and bbb are integers.

STEP 3

Apply the exponentiation rule to the given expression.x97=x97x^{\frac{9}{7}} = \sqrt[7]{x^{9}}x79​=7x9​

STEP 4

Now, we need to simplify x97\sqrt[7]{x^{9}}7x9​ if possible. We can rewrite x9x^{9}x9 as x7⋅x2x^{7} \cdot x^{2}x7⋅x2 because 9=7+29 = 7 + 29=7+2.

STEP 5

Substitute x9x^{9}x9 with x7⋅x2x^{7} \cdot x^{2}x7⋅x2 in the radical expression.x97=x7⋅x27\sqrt[7]{x^{9}} = \sqrt[7]{x^{7} \cdot x^{2}}7x9​=7x7⋅x2​

STEP 6

According to the properties of radicals, x7⋅x27\sqrt[7]{x^{7} \cdot x^{2}}7x7⋅x2​ can be split into the product of two radicals: x77⋅x27\sqrt[7]{x^{7}} \cdot \sqrt[7]{x^{2}}7x7​⋅7x2​.

STEP 7

Simplify the first radical. Since the index of the radical and the exponent are the same, x77=x\sqrt[7]{x^{7}} = x7x7​=x.

STEP 8

Combine the simplified radicals.x7⋅x27=x⋅x27\sqrt[7]{x^{7} \cdot x^{2}} = x \cdot \sqrt[7]{x^{2}}7x7⋅x2​=x⋅7x2​

STEP 9

Now, we compare the expression we have obtained with the given options.

STEP 10

We see that x⋅x27x \cdot \sqrt[7]{x^{2}}x⋅7x2​ matches option B.x⋅x27=xx27x \cdot \sqrt[7]{x^{2}} = x \sqrt[7]{x^{2}}x⋅7x2​=x7x2​

STEP 11

Select the correct answer based on the comparison.The correct answer is B. xx27x \sqrt[7]{x^{2}}x7x2​.

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

Rewrite the expression $x^{\frac{9}{7}}$ . Select the correct answer: A. $\left(\frac{1}{\sqrt{x}}\right)^{9}$ , B. $x \sqrt[7]{x^{2}}$ , C. $\sqrt[9]{x^{7}}$ , D. $x \sqrt[7]{x}$ .

Assumptions
1. We need to rewrite the expression $x^{\frac{9}{7}}$ in a different form.
2. We are given multiple choice answers and must select the correct one.

Understand the exponentiation rules that can be used to rewrite the expression. The expression $x^{\frac{9}{7}}$ can be rewritten using the rule $x^{\frac{a}{b}} = \sqrt[b]{x^{a}}$ , where $a$ and $b$ are integers.

Apply the exponentiation rule to the given expression.
$x^{\frac{9}{7}} = \sqrt[7]{x^{9}}$

Now, we need to simplify $\sqrt[7]{x^{9}}$ if possible. We can rewrite $x^{9}$ as $x^{7} \cdot x^{2}$ because $9 = 7 + 2$ .

Substitute $x^{9}$ with $x^{7} \cdot x^{2}$ in the radical expression.
$\sqrt[7]{x^{9}} = \sqrt[7]{x^{7} \cdot x^{2}}$

According to the properties of radicals, $\sqrt[7]{x^{7} \cdot x^{2}}$ can be split into the product of two radicals: $\sqrt[7]{x^{7}} \cdot \sqrt[7]{x^{2}}$ .

Simplify the first radical. Since the index of the radical and the exponent are the same, $\sqrt[7]{x^{7}} = x$ .

Combine the simplified radicals.
$\sqrt[7]{x^{7} \cdot x^{2}} = x \cdot \sqrt[7]{x^{2}}$

We see that $x \cdot \sqrt[7]{x^{2}}$ matches option B.
$x \cdot \sqrt[7]{x^{2}} = x \sqrt[7]{x^{2}}$

Select the correct answer based on the comparison.
The correct answer is B. $x \sqrt[7]{x^{2}}$ .