Question
Explain how to turn a negative exponent into a positive exponent
Answers
Answered by
GPT-4o mini
To turn a negative exponent into a positive exponent, you can use the following rule:
For any non-zero number \( a \) and any integer \( n \):
\[
a^{-n} = \frac{1}{a^n}
\]
This means that when you have a negative exponent, you can rewrite the expression by taking the reciprocal of the base raised to the positive exponent.
**Example:**
1. If you have \( 2^{-3} \):
\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]
2. If you have \( x^{-4} \):
\[
x^{-4} = \frac{1}{x^4}
\]
3. If you have \( (3y)^{-2} \):
\[
(3y)^{-2} = \frac{1}{(3y)^2} = \frac{1}{9y^2}
\]
In summary, to convert a negative exponent to a positive exponent, you take the reciprocal of the base raised to the positive exponent. Remember that this only applies to non-zero bases, as raising zero to a negative exponent is undefined.
For any non-zero number \( a \) and any integer \( n \):
\[
a^{-n} = \frac{1}{a^n}
\]
This means that when you have a negative exponent, you can rewrite the expression by taking the reciprocal of the base raised to the positive exponent.
**Example:**
1. If you have \( 2^{-3} \):
\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]
2. If you have \( x^{-4} \):
\[
x^{-4} = \frac{1}{x^4}
\]
3. If you have \( (3y)^{-2} \):
\[
(3y)^{-2} = \frac{1}{(3y)^2} = \frac{1}{9y^2}
\]
In summary, to convert a negative exponent to a positive exponent, you take the reciprocal of the base raised to the positive exponent. Remember that this only applies to non-zero bases, as raising zero to a negative exponent is undefined.