Final answer:
To simplify the expression (5^-²)⁵ x 5⁴, first convert the negative exponent to a fraction and then simplify the expression by multiplying the bases and adding the exponents.
Step-by-step explanation:
To simplify the expression (5^-²)⁵ x 5⁴, first consider the negative exponent.
Whenever a number has a negative exponent, it should be moved to the opposite position in the fraction. So, 5^-² becomes 1/5², which is equal to 1/25.
Next, simplify the expression by multiplying (1/25)⁵ x 5⁴. Since the base is the same, we can add the exponents, giving us (1/25)⁸. Finally, simplify further by multiplying the numerators and the denominators: 1⁸ / 25⁸. This gives us the answer of 1/25⁸.