Answer:
These expressions have a value of - 1/64:
A. (- 1/4) ³
B. - (1/4) ³
D. - (1/8) ²
F. - (1/2) ⁶
Step-by-step explanation:
1. Let's resolve each one to understand which of these expressions meet the value of - 1/64
A. (- 1/4) ³ = ( - 1/4 * - 1/4 * - 1/4) = ( -1 * -1 *- 1/ 4 * 4 * 4) = - 1/64 (Note that the negative sign is inside the parenthesis and it changes two times but the final outcome is - ). So this expression has a value of - 1/64
B. - (1/4) ³ = - ( 1/4 * 1/4 * 1/4) = - (1 * 1 * 1/ 4 * 4 * 4) = - 1/64 (Note that the negative sign is outside the parenthesis and it remains negative because the result inside the parenthesis is positive). So this expression has a value of - 1/64
C. (-1/8) ² = ( - 1/8 * - 1/8 ) = ( -1 * -1 / 8 * 8) = 1/64 (Note that the negative sign is inside the parenthesis and it changes because the final outcome is +). So this expression hasn't a value of - 1/64
D. - (1/8) ² = - ( 1/8 * 1/8 ) = - (1 * 1 / 8 * 8) = - 1/64 (Note that the negative sign is outside the parenthesis and it remains negative because the result inside the parenthesis is positive ). So this expression has a value of - 1/64
E. (- 1/2) ⁶ = (- 1/2 * -1/2 * -1/2 * -1/2 * -1/2 * -1/2) = (-1 *- 1 *- 1 * -1 * -1 * -1/ 2 * 2 * 2 * 2 * 2 * 2) = 1/64 (Note that the negative sign is inside the parenthesis and it changes because the final outcome is + ). So this expression hasn't a value of - 1/64
F. - (1/2) ⁶ = - ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2) = - (1 * 1 * 1 * 1 * 1 * 1/ 2 * 2 * 2 * 2 * 2 * 2) = - 1/64 (Note that the negative sign is outside the parenthesis and it remains negative because the result inside the parenthesis is positive ). So this expression has a value of - 1/64.
