Question

Solve the following expressions with (-2) and (-3):

A) (-2)⁵ = -32; (-3)⁵ = -243
B) (-2)⁵ = -64; (-3)⁵ = -243
C) (-2)⁵ = 32; (-3)⁵ = 243
D) (-2)⁵ = 64; (-3)⁵ = 243

Answer 1

The correct expressions when solving for (-2) raised to the fifth power and (-3) raised to the fifth power are (-2)⁵ = -32 and (-3)⁵ = -243.

Step-by-step explanation:

The student's question involves solving the expressions for negative bases raised to an odd power. When raising a negative number to an odd power, the result will also be negative. Therefore, in this case:

• (-2)⁵ = -2 × -2 × -2 × -2 × -2 = -32 since multiplying four negative numbers results in a positive number, but multiplying that by one more negative number makes it negative again.
• (-3)⁵ = -3 × -3 × -3 × -3 × -3 = -243 for the same reasoning as above.

Based on this explanation, the correct answer is:

A) (-2)⁵ = -32; (-3)⁵ = -243.