(2^5)^3 * 2^(-7) / 2^(-6)

To solve the expression ( 2 5 ) 3 × 2 − 7 ÷ 2 − 6 , we need to use the properties of exponents. Let's break it down step-by-step:

Simplify ( 2 5 ) 3 : According to the power of a power property, ( a m ) n = a m × n . Applying this to ( 2 5 ) 3 , we get: ( 2 5 ) 3 = 2 5 × 3 = 2 15

Multiply by 2 − 7 : We apply the product of powers property: a m × a n = a m + n . So: 2 15 × 2 − 7 = 2 15 + ( − 7 ) = 2 8

Divide by 2 − 6 : Using the quotient of powers property: a m ÷ a n = a m − n . Therefore: 2 − 6 2 8 ​ = 2 8 − ( − 6 ) = 2 8 + 6 = 2 14


Therefore, the simplified expression is 2 14 . The value of 2 14 is quite large, but if needed, it can be calculated numerically as: 2 14 = 16384
So, the final result of the expression is 2 14 = 16384 . This demonstrates the proper application of exponent rules to simplify expressions.

Answered by JessicaJessy | 2025-07-06