GATE 2023 BT – Question 34
If $7^{3x}=216$, the value of $7^{-x}$ (rounded off to three decimal places) is ____________.
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Correct answer: 0.157 to 0.177
Explanation
**Step 1: recognise 216.** $216=6^3$.
**Step 2: rewrite the equation.**
$$7^{3x}=\left(7^x\right)^3=6^3\;\Rightarrow\;7^x=6 .$$
**Step 3: the quantity asked for.**
$$7^{-x}=\frac1{7^x}=\frac16=0.1667\approx\mathbf{0.167}.$$