Question

If \(7^{3x}=216\), the value of \(7^{-x}\) (rounded off to three decimal places) is __________________.

Hint:

- If \(a^{3x}=b\), then \(a^{x}=b^{1/3}\).
- Compute the required power using reciprocals: \(a^{-x}=\frac{1}{a^x}\).

Answer 1

Correct Answer: 0.166

Step 1: From \(7^{3x}=216\Rightarrow 7^{x}=216^{1/3}=6\).
Step 2: Therefore \(7^{-x}=\dfrac{1}{7^{x}}=\dfrac{1}{6}=0.166\overline{6}\approx 0.167\) (3 d.p.).