Practice Solving Problems with Negative Exponents

Select the equivalent expression.

1. \(x^{-6}=?\)

   Choose 1 answer:
   

   1. \(6^x\)
   2. \((-x)^6\)
   3. \(\frac{1}{x^6}\)

2. \(2^{-4}=?\)

   Choose 1 answer:
   

   1. \((-2)^{4}\)
   2. \(-2^{4}\)

   3. \(\dfrac{1}{2^{4}}\)

3. \(\dfrac{1}{a^7}=?\)

   Choose 1 answer:
   

   1. \(a^{-7}\)
   2. \(a^{^{\frac17}}\)

   3. \(7^a\)

4. \(\dfrac{1}{9^{2}}=?\)

   Choose 1 answer:
   

   1. \(9^{^{\frac1{2}}}\)
   2. \(\dfrac{1^{2}}{9}\)
   3. \(9^{-{2}}\)

Source: Khan Academy, https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-negative-exponents/e/exponents_2
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1. This is the definition for negative exponents:

   \(x^{-n}=\dfrac{1}{x^n}\)

   \(x^{-6}=\dfrac{1}{x^{6}}\)

2. This is the definition for negative exponents:

   \(x^{-n}=\dfrac{1}{x^n}\)

   \(2^{-4}=\dfrac{1}{2^{4}}\)

3. This is the definition for negative exponents:

   \(x^{-n}=\dfrac{1}{x^n}\)

   Applying the definition in the reverse direction, we get
   

   \(\dfrac{1}{a^7}=a^{-7}\)

4. This is the definition for negative exponents:

   \(x^{-n}=\dfrac{1}{x^n}\)

   Applying the definition in the reverse direction, we get:
   

   \(\dfrac{1}{9^{2}}=9^{-{2}}\)