How would I find three different quotients that equal 5 to the negative 7th
how about 5^2 ÷ 5^9 = 5^(2-9) = 5^-7
remember you have to subtract the exponents, so any other combination that will give you an exponent of -7 will do
Try it.
To find three different quotients that equal 5 to the power of -7, you can start with the expression 5^(-7) and divide it by three different numbers. Here's how you can approach it:
1. Quotient with 5: Divide 5^(-7) by 5.
- The expression 5^(-7) can be rewritten as 1/(5^7).
- Divide 1/(5^7) by 5 to get 1/(5^7 * 5) or 1/(5^8). This is one quotient that equals 5^(-7).
2. Quotient with 25: Divide 5^(-7) by 25.
- The expression 5^(-7) can be rewritten as 1/(5^7).
- Divide 1/(5^7) by 25 to get 1/(25 * 5^7) or 1/(5^2 * 5^7) or 1/(5^9). This is another quotient that equals 5^(-7).
3. Quotient with 125: Divide 5^(-7) by 125.
- The expression 5^(-7) can be rewritten as 1/(5^7).
- Divide 1/(5^7) by 125 to get 1/(125 * 5^7) or 1/(5^3 * 5^7) or 1/(5^10). This is a third quotient that equals 5^(-7).
So, three different quotients that equal 5^(-7) are: 1/(5^8), 1/(5^9), and 1/(5^10).