Simplify the expression completely:

(a-4⋅b7)-4 =

To simplify the expression \( (a - 4 \cdot b^7)^{-4} \), we will follow the rule of exponents.

### Step 1: Apply the exponent
The expression has a negative exponent of \(-4\), which can be handled by applying the following rule:

\[
(x)^{-n} = \frac{1}{x^n}
\]

Thus, we rewrite the expression as:

\[
(a - 4 \cdot b^7)^{-4} = \frac{1}{(a - 4 \cdot b^7)^4}
\]

### Final Answer:
\[
\frac{1}{(a - 4 \cdot b^7)^4}
\]

This is the fully simplified form of the expression.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify expressions with negative exponents?
2. What is the general rule for raising a binomial to a power?
3. How do you expand \( (a - b)^n \) using the binomial theorem?
4. Can you explain how to handle fractional exponents?
5. What is the difference between simplifying \( x^{-n} \) and \( (x - y)^{-n} \)?

**Tip:** Always remember that a negative exponent in an expression can be rewritten as a reciprocal to eliminate the negative sign.

Simplify the expression completely: (a - 4⋅b^7)^-4 =

Learn how to simplify the expression (a - 4b^7)^-4 using exponent rules. This problem covers key algebraic concepts like negative exponents and binomial exponentiation. Suitable for students in Grades 9-11.

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