Exponent Expression 7D5573

1. **State the problem:** We want to find an expression equivalent to $$2^{-7} \cdot \frac{2^{-7}}{2^{0}}$$. 2. **Recall the exponent rules:** - When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$. - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Any number to the zero power is 1: $$a^0 = 1$$. 3. **Simplify the denominator:** Since $$2^0 = 1$$, the expression becomes: $$2^{-7} \cdot \frac{2^{-7}}{1} = 2^{-7} \cdot 2^{-7}$$. 4. **Multiply the powers:** Using the multiplication rule: $$2^{-7} \cdot 2^{-7} = 2^{-7 + (-7)} = 2^{-14}$$. 5. **Rewrite the expression:** $$2^{-14} = \frac{1}{2^{14}}$$. **Final answer:** $$\frac{1}{2^{14}}$$.