Final answer:
The expression (−7)⁵/³⋅(1/56)⁵/³ simplifies to (−1/2)⁵ which equals −0.03125 when fully evaluated.
Step-by-step explanation:
We have been asked to evaluate the expression (−7)⁵/³⋅(1/56)⁵/³. This expression can be simplified by considering the exponent rules for multiplication and division of powers with the same base.
Firstly, note that (−7)⁵/³ represents the cube root of −7 raised to the power of 5, which is − 7 ⁵/³, and the same logic applies to (1/56)⁵/³.
Since −7 and 1/56 are separately raised to the same power, we can combine them first before applying the power:
−7 × 1/56 = −7 / 56
Now, (−7 / 56)⁵/³ is equal to (-1/8)⁵/³, because -7 × 8 = -56. We now find the cube root of -1/8, which is -1/2, and then raise this to the 5th power.
The cube root of -1/8 is -1/2 and raising -1/2 to the 5th power gives us:
(−1/2)⁵ = −0.5 ⁵ = −0.03125
Therefore, the evaluated expression is −0.03125.