1. **State the problem:** Calculate the value of the expression $$[(-7)^2 - (-2)^6]^2$$. 2. **Recall the rules:** - When raising a negative number to an even power, the result is positive. - Calculate powers first, then perform subtraction, and finally square the result. 3. **Calculate each power:** $$(-7)^2 = (-7) \times (-7) = 49$$ $$(-2)^6 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2) = 64$$ 4. **Substitute back into the expression:** $$[49 - 64]^2$$ 5. **Simplify inside the brackets:** $$49 - 64 = -15$$ 6. **Square the result:** $$(-15)^2 = (-15) \times (-15) = 225$$ **Final answer:** $$225$$