Question:
What is the value of \( x \) in the following equation?
\[
\frac{x^{0.4}}{16} = \frac{32}{x^{2.6}}
\]
What is the value of \( x \) in the following equation?
\[
\frac{x^{0.4}}{16} = \frac{32}{x^{2.6}}
\]
Show Hint
When you see exponents on both sides, try combining like bases using exponent rules and simplify.
Updated On: Aug 7, 2025
- 8
- 9
- 6
- 7
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The Correct Option is A
Solution and Explanation
Start with:
\[
\frac{x^{0.4}}{16} = \frac{32}{x^{2.6}}
\]
Multiply both sides by \(16x^{2.6}\) to eliminate denominators:
\[
x^{0.4} \cdot x^{2.6} = 32 \cdot 16
\Rightarrow x^{3} = 512
\]
Now take cube root on both sides:
\[
x = \sqrt[3]{512} = \boxed{8}
\]
\fbox{Final Answer: (A) 8}
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