I am not sure how to write a fraction as an expression using a negative number for an exponent other than
-1? Please help ex: 1/25 and then using a fraction of 1/9to the second power.
To write a fraction as an expression using a negative number for an exponent, you can follow these steps:
1. Start with the given fraction. Let's take the example of 1/25.
2. Determine the base of the fraction. In this case, the base is 1/25.
3. Write the base raised to the negative exponent. If the exponent is -1, it means taking the reciprocal of the base. For example, 1/25 to the power of -1 would be written as the reciprocal of 1/25, which is 25/1.
4. If the exponent is a number other than -1, you can use the property of exponents which states that x^(-n) is equal to 1/x^n. In other words, to write a fraction with a negative exponent, you can rewrite it as the reciprocal of the fraction with the positive exponent. For example, 1/9 raised to the power of -2 would be written as 1/(1/9)^2.
Let's apply these steps to the examples you provided:
1. 1/25:
- The base is 1/25.
- To write it as an expression with a negative exponent, we take the reciprocal: (1/25)^-1 = 25/1.
2. 1/9^2:
- The base is 1/9.
- The exponent is 2, and since it's positive, we don't need to change the sign.
- To write it as an expression with a negative exponent, we rewrite it as the reciprocal: 1/(1/9)^2 = 1/(1/81) = 81/1.
Remember, when dealing with negative exponents, you are essentially manipulating the fraction by taking the reciprocal or rewriting it as the reciprocal of the positive exponent expression.