To calculate \( 0.06^{-4} \), we can use the property of negative exponents:

\[
a^{-n} = \frac{1}{a^n}
\]

So,

\[
0.06^{-4} = \frac{1}{0.06^4}
\]

Now let's calculate \( 0.06^4 \):

\[
0.06^4 = (0.06) \times (0.06) \times (0.06) \times (0.06)
\]

Let me calculate that for you.

\[
0.06^4 = 0.00001296
\]

Now, find the reciprocal:

\[
0.06^{-4} = \frac{1}{0.00001296} \approx 77160.49
\]

Thus, \( 0.06^{-4} \approx 77160.49 \).

Would you like a detailed explanation on any step?

Here are 5 questions related to negative exponents:
1. What is the value of \( 0.05^{-3} \)?
2. How do you simplify \( 2^{-5} \)?
3. What is \( (-0.07)^{-2} \)?
4. How does \( x^{-1} \) behave as \( x \) approaches 0?
5. What is the general rule for negative exponents?

**Tip:** Always remember, a negative exponent means taking the reciprocal of the base raised to the positive exponent.

Learn how to solve 0.06 raised to the power of -4 using the negative exponent rule. Follow a step-by-step guide to calculate the reciprocal and find that 0.06^-4 ≈ 77160.49. This solution covers key concepts of exponents and negative powers. Suitable for Grades 7-10.

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