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The ratio x:64x : 64 is equivalent to the ratio 64:x264 : x^2. What is that value of xx?

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Full solution

Q. The ratio x:64x : 64 is equivalent to the ratio 64:x264 : x^2. What is that value of xx?
  1. Set up proportion: Set up the proportion based on the given ratios.\newlineThe given ratios are x:64x : 64 and 64:x264 : x^2. Since they are equivalent, we can write the proportion as x64=64x2\frac{x}{64} = \frac{64}{x^2}.
  2. Cross-multiply to solve: Cross-multiply to solve for xx. Cross-multiplying gives us x×x2=64×64x \times x^2 = 64 \times 64.
  3. Simplify the equation: Simplify the equation.\newlineSimplifying the left side of the equation by multiplying xx by x2x^2 gives us x3=64×64x^3 = 64 \times 64.
  4. Calculate value: Calculate the value of 64×6464 \times 64.\newline64×6464 \times 64 equals 40964096, so the equation now is x3=4096x^3 = 4096.
  5. Take cube root: Take the cube root of both sides to solve for xx.\newlineTaking the cube root of 40964096 gives us x=16x = 16, since 16×16×16=409616 \times 16 \times 16 = 4096.

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