Question

Negative Integer Exponents Practice Anwers

Answer 1

Certainly! Negative integer exponents can be tricky at first, but with practice, they become easier to understand. A negative exponent indicates that the base should be taken as the reciprocal. In other words, \( a^{-n} = \frac{1}{a^n} \) for any nonzero number \( a \) and any positive integer \( n \).

Here are some practice problems with negative integer exponents, along with their answers:

### Practice Problems

1. \( 2^{-3} \)
2. \( 5^{-2} \)
3. \( x^{-4} \)
4. \( (3^{-1})^2 \)
5. \( 10^{-1} + 10^{-2} \)
6. \( (a^{-2}b^{-3})^{-1} \)
7. \( (7^{-1} + 2^{-1})^{-1} \)
8. \( (4^{-3})^{-2} \)

### Answers

1. \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
2. \( 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \)
3. \( x^{-4} = \frac{1}{x^4} \)
4. \( (3^{-1})^2 = ( \frac{1}{3} )^2 = \frac{1}{9} \)
5. \( 10^{-1} + 10^{-2} = \frac{1}{10} + \frac{1}{100} = \frac{10}{100} + \frac{1}{100} = \frac{11}{100} \)
6. \( (a^{-2}b^{-3})^{-1} = a^2b^3 \)
7. \( (7^{-1} + 2^{-1})^{-1} = ( \frac{1}{7} + \frac{1}{2} )^{-1} = ( \frac{2 + 7}{14} )^{-1} = \frac{14}{9} \)
8. \( (4^{-3})^{-2} = ( \frac{1}{4^3} )^{-2} = 4^{3 \times 2} = 4^6 = 4096 \)

Feel free to ask for more practice problems or explanations!