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Write [(-4) x (-5)]⁵ as a product of powers

A.(-4)⁵ + (-5)⁵
B.5(-4) + 5(-5)
C.(-4)⁵ x (-5)⁵
D.4⁵ x 5⁵

User Lonzo
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1 Answer

1 vote

Final answer:

The expression [(-4) x (-5)]⁵ is correctly written as (-4)⁵ x (-5)⁵, as per the multiplication rules for negative numbers and exponentiation, which corresponds to option C.

Step-by-step explanation:

The expression [(-4) x (-5)]⁵ can be represented as a product of powers. When two negative numbers are multiplied, the result is positive according to multiplication rules. Therefore, (-4) multiplied by (-5) gives us 20. Now raising this to the power of 5 means multiplying 20 by itself 5 times, which is the same as raising 4 to the power of 5 and 5 to the power of 5 separately and then multiplying them because the base 20 is a product of 4 and 5. Thus,

(-4) x (-5) = 4 x 5 = 20

and

20⁵ = (4⁵) x (5⁵).

Therefore, the correct answer is (-4)⁵ x (-5)⁵, which corresponds to option C.

User James Bell
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