What is the smallest positive integer solution to $\left(\frac{100,000,000}{x^{4}}\right)

Q: What is the smallest positive integer solution to $\left(\frac{100,000,000}{x^{4}}\right)<1$ ?

∻Solution by Steps∻ ‖ step 1 ⋮ To find the smallest positive integer solution, we start by solving the inequality $$\left(\frac{100,000,000}{x^{4}}\right) \sqrt[4]{100,000,000}$$. ‖ ‖ step 4 ⋮ Calculate the fourth root of 100,000,000 to get $$x > 100$$. ‖ ‖ step 5 ⋮ Since we are looking for the smallest positive integer solution, the answer is the smallest integer greater than 100, which is 101. ‖ ∻Answer∻ ⚹ 101 ⚹ ∻Key Concept∻ ⚹Solving Inequalities Involving Powers⚹ ∻Explanation∻ ⚹To solve the inequality, we isolated the variable by multiplying both sides by $$x^4$$ and then took the fourth root to find the range of solutions. We then identified the smallest integer greater than 100 to find the smallest positive integer solution.⚹◊What is the value of $x$ when solving for the smallest positive integer solution to the inequality $\left(\frac{100000000}{x^{4}}\right)

Question

What is the smallest positive integer solution to $\left(\frac{100,000,000}{x^{4}}\right)<1$ ?

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the smallest positive integer solution, we start by solving the inequality $$\left(\frac{100,000,000}{x^{4}}\right)<1$$. ‖ ‖ step 2 ⋮ Multiply both sides of the inequality by $$x^4$$ to get $$100,000,000 < x^4$$. ‖ ‖ step 3 ⋮ Take the fourth root of both sides to find $$x > \sqrt[4]{100,000,000}$$. ‖ ‖ step 4 ⋮ Calculate the fourth root of 100,000,000 to get $$x > 100$$. ‖ ‖ step 5 ⋮ Since we are looking for the smallest positive integer solution, the answer is the smallest integer greater than 100, which is 101. ‖ ∻Answer∻ ⚹ 101 ⚹ ∻Key Concept∻ ⚹Solving Inequalities Involving Powers⚹ ∻Explanation∻ ⚹To solve the inequality, we isolated the variable by multiplying both sides by $$x^4$$ and then took the fourth root to find the range of solutions. We then identified the smallest integer greater than 100 to find the smallest positive integer solution.⚹◊What is the value of $x$ when solving for the smallest positive integer solution to the inequality $\left(\frac{100000000}{x^{4}}\right)<1$?⍭ Generate me a similar question◊

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