Let's break down the expression \(\left(\frac{1}{7}\right)^4 (-7)^2\).

1. First, calculate \(\left(\frac{1}{7}\right)^4\):

\[
\left(\frac{1}{7}\right)^4 = \frac{1}{7^4} = \frac{1}{2401}
\]

2. Now calculate \((-7)^2\):

\[
(-7)^2 = 49
\]

3. Multiply the results together:

\[
\frac{1}{2401} \times 49 = \frac{49}{2401}
\]

Simplifying \(\frac{49}{2401}\):

\[
\frac{49}{2401} = \frac{49}{49 \times 49} = \frac{1}{49}
\]

So, the final result is:

\[
\frac{1}{49}
\]

Would you like further details on any part of the solution?

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Here are 5 related questions you could explore:
1. How do you simplify an expression with negative exponents?
2. What is the general rule for multiplying fractions with powers?
3. How do powers of negative numbers behave for even and odd exponents?
4. Can you calculate \(\left(\frac{2}{5}\right)^3 (-5)^4\)?
5. What happens when a fraction is raised to a negative power?

**Tip:** When raising fractions to a power, both the numerator and denominator are raised to the same power.

Learn how to simplify the exponential expression (1/7)^4 (-7)^2 using properties of exponents and fractions. This solution walks through step-by-step calculations, including multiplying fractions and handling negative numbers. Suitable for students in Grades 7-9.

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