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Answer :
To solve the equation [tex]\(\sqrt[3]{x^4} = 625\)[/tex], we need to find the value of [tex]\(x\)[/tex] that satisfies this equation. Let's break down the solution step-by-step:
1. Understanding the Equation:
The given equation is [tex]\(\sqrt[3]{x^4} = 625\)[/tex]. This means that we are dealing with the cube root of [tex]\(x^4\)[/tex].
2. Remove the Cube Root:
To eliminate the cube root, we can raise both sides of the equation to the power of 3. This results in:
[tex]\[(x^4)^{1/3}^3 = 625^3\][/tex]
3. Simplify the Left Side:
The left side simplifies because [tex]\((x^4)^{1/3}\)[/tex] raised to the third power is just [tex]\(x^4\)[/tex]:
[tex]\[x^4 = 625^3\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Now we have the equation [tex]\(x^4 = 625^3\)[/tex]. We need to find the fourth root of [tex]\(625^3\)[/tex] to solve for [tex]\(x\)[/tex].
5. Calculate the Fourth Root:
We take the fourth root of both sides. Since [tex]\(x^4 = 625^3\)[/tex], solving for [tex]\(x\)[/tex] gives:
[tex]\[x = (625^3)^{1/4}\][/tex]
By calculating this step, we find that:
[tex]\[x = 125\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\sqrt[3]{x^4} = 625\)[/tex] is [tex]\(x = 125\)[/tex].
1. Understanding the Equation:
The given equation is [tex]\(\sqrt[3]{x^4} = 625\)[/tex]. This means that we are dealing with the cube root of [tex]\(x^4\)[/tex].
2. Remove the Cube Root:
To eliminate the cube root, we can raise both sides of the equation to the power of 3. This results in:
[tex]\[(x^4)^{1/3}^3 = 625^3\][/tex]
3. Simplify the Left Side:
The left side simplifies because [tex]\((x^4)^{1/3}\)[/tex] raised to the third power is just [tex]\(x^4\)[/tex]:
[tex]\[x^4 = 625^3\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Now we have the equation [tex]\(x^4 = 625^3\)[/tex]. We need to find the fourth root of [tex]\(625^3\)[/tex] to solve for [tex]\(x\)[/tex].
5. Calculate the Fourth Root:
We take the fourth root of both sides. Since [tex]\(x^4 = 625^3\)[/tex], solving for [tex]\(x\)[/tex] gives:
[tex]\[x = (625^3)^{1/4}\][/tex]
By calculating this step, we find that:
[tex]\[x = 125\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\sqrt[3]{x^4} = 625\)[/tex] is [tex]\(x = 125\)[/tex].
Thank you for reading the article Complete the pairs by finding the corresponding value of tex tex Match the Zoomed Expression tex sqrt 3 x 4 625 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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