Simplify x^-a: Understanding Negative Exponent Notation

Question

$x^{-a}=\text{?}$

Video Solution

Solution Steps

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 Solution

We use the exponential property of a negative exponent:

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

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

Answer

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

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Question Types

Negative Exponents: Calculating powers with negative exponents Negative Exponents: Presenting powers with negative exponents as fractions Negative Exponents: Presenting powers with negative exponents as fractions Negative Exponents: Using variables Applying Combined Exponents Rules: Calculating powers with negative exponents Applying Combined Exponents Rules: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Two Variables Applying Combined Exponents Rules: Using variables Applying Combined Exponents Rules: Variable in the exponent of the power