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:
   

   $$\dfrac{1}{9^{2}}=9^{-{2}}$$