Question

#3.PROBLEMVALUEDECISION3 to the negative 2nd power1 ninthCORRECT!2 to the negative 3rd power1 eighthCORRECT!10 to the negative 1st powerStartFraction, 1 Over 10 , EndFractionCORRECT!"x" to the negative 2nd powerMath Input:"x" to the negative 3rd powerMath Input:"x" to the negative 4th powerMath Input:"x" to the negative 13th powerMath Input:"x" to the negative 1st powerMath Input:A few examples of expressions with negative exponents are given. Complete the table.PRO-TIP: use / to build a fraction.

Answer 1

Sure! Let’s complete the table based on the expressions you provided with negative exponents.

Here's how to convert expressions with negative exponents into fractional form:

1. \( a^{-n} = \frac{1}{a^{n}} \)
2. If \( a = 2 \) and \( n = 2 \), then \( 2^{-2} = \frac{1}{2^{2}} = \frac{1}{4} \)
3. If \( a = 3 \) and \( n = 3 \), then \( 3^{-3} = \frac{1}{3^{3}} = \frac{1}{27} \)
4. If \( a = 10 \) and \( n = 1 \), then \( 10^{-1} = \frac{1}{10^{1}} = \frac{1}{10} \)
5. If you have a variable \( x \):
   • \( x^{-1} = \frac{1}{x^{1}} = \frac{1}{x} \)
   • \( x^{-2} = \frac{1}{x^{2}} \)
   • \( x^{-3} = \frac{1}{x^{3}} \)
   • \( x^{-4} = \frac{1}{x^{4}} \)
   • \( x^{-13} = \frac{1}{x^{13}} \)

Here’s the completed table based on your examples:

| Expression | Fraction | |------------------------|------------------------| | \( 2^{-2} \) | \( \frac{1}{4} \) | | \( 2^{-3} \) | \( \frac{1}{8} \) | | \( 10^{-1} \) | \( \frac{1}{10} \) | | \( x^{-2} \) | \( \frac{1}{x^{2}} \) | | \( x^{-3} \) | \( \frac{1}{x^{3}} \) | | \( x^{-4} \) | \( \frac{1}{x^{4}} \) | | \( x^{-13} \) | \( \frac{1}{x^{13}} \) | | \( x^{-1} \) | \( \frac{1}{x} \) |

If you have any specific expressions that we need to talk about or if you need more help, just let me know!