Simplify x^-a: Understanding Negative Exponent Notation

x−a=? x^{-a}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following expression
00:03 According to the laws of exponents, any number(A) raised to the power of(N)
00:07 equals 1 divided by the number(A) raised to the power of(-N)
00:10 Let's apply this to the question
00:13 The number(X) becomes 1 divided by X
00:16 And the exponent(-A) becomes -(-A)
00:19 A negative multiplied by a negative becomes a positive hence the power is A
00:22 This is the solution

Step-by-step written solution

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1

Understand the problem

x−a=? x^{-a}=\text{?}

2

Step-by-step solution

We use the exponential property of a negative exponent:

b−n=1bn b^{-n}=\frac{1}{b^n} We apply it to the problem:

x−a=1xa x^{-a}=\frac{1}{x^a} Therefore, the correct answer is option C.

3

Final Answer

1xa \frac{1}{x^a}

Practice Quiz

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\( (4^3)^2= \)

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