Multiply Powers: Solving (-1)^99 × (-1)^9

(1)99(1)9= (-1)^{99}\cdot(-1)^9=

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Step-by-step video solution

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00:00 Solve
00:04 First let's calculate the signs
00:07 Odd power, therefore the sign remains negative
00:21 This applies to both powers
00:29 1 to any power is always equal to 1
00:43 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

(1)99(1)9= (-1)^{99}\cdot(-1)^9=

2

Step-by-step solution

To solve this problem, we need to evaluate the expression (1)99(1)9 (-1)^{99} \cdot (-1)^9 .

The first step is to evaluate each component:

  • Step 1: Evaluate (1)99 (-1)^{99} .
    Since 99 is an odd number, (1)99=1(-1)^{99} = -1. This is because any odd power of 1-1 results in 1-1.
  • Step 2: Evaluate (1)9 (-1)^9 .
    Similarly, since 9 is also an odd number, (1)9=1(-1)^9 = -1. Again, an odd exponent means the result is 1-1.

Step 3: Multiply the results from step 1 and step 2:
(1)99(1)9=(1)(1)=1 (-1)^{99} \cdot (-1)^9 = (-1) \cdot (-1) = 1 .

Thus, the value of the expression is 1\boxed{1}.

3

Final Answer

1 1

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\( (-2)^7= \)

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