Question

simplify and express the result with positive exponents

Answer 1

$( {2}^{ - 7} \div {2}^{ - 9} ) \times {2}^{ - 4} \\ = {2}^{ - 7 - ( - 9)} \times {2}^{ - 4} \\ = {2}^{ - 7 + 9} \times {2}^{ - 4} \\ = {2}^{2} \times {2}^{ - 4} \\ = {2}^{2 - 4} \\ = {2}^{ - 2} \\ = { (\frac{1}{2}) }^{2}$

Answer 2

2 raised to the power -7 can be written as 1/128.
2 raised to the power -9 can be written as 1/512.
1/128÷1/512 = 1/128×512 = 4
4×2raised to -4 is 4×1/16 = 1/4