which expression is equivalent to 2^7·2^(-10)?\n1/2^70\n1/2^3\n1/2^(-3)\n1/2^(-70)

Explanation:

Step1: Apply exponent - product rule

According to the rule (a^m\cdot a^n=a^{m + n}), for (a = 2), (m = 7) and (n=-10), we have (2^7\cdot2^{-10}=2^{7+( - 10)}).

Step2: Calculate the exponent

(7+( - 10)=7 - 10=-3), so (2^{7+( - 10)}=2^{-3}).

Step3: Use negative - exponent rule

The negative - exponent rule is (a^{-n}=\frac{1}{a^n}), so (2^{-3}=\frac{1}{2^3}).

Answer:

(\frac{1}{2^3})