Question

What is 5 to the power of 3 over five to the power of 7 in index form

Answer 1

5 to the power of 3 over five to the power of 7 in index form is
`5^/[(-4)}`h is obtained by subtracting the exponent in the denominator (7) from the exponent in the numerator (3).

Step-by-step explanation:

The student has asked what is 5 to the power of 3 over five to the power of 7 in index form. To answer this question, we use the laws of exponents which state that when dividing powers with the same base, you subtract the exponents. In mathematical form:

`5^3`5^7 =
`5^(3-7)`

This is because the exponent of the numerator (3) is subtracted from the exponent of the denominator (7), which yields an exponent of -4. When expressed in index form, the answer is 5 to the power of negative 4, which can also be written as 1/5^4
`5^{(-4)` if you prefer positive exponents.

Answer 2

5 to the third power over 7 in index form is 125 over 7 and indexed it will be -125 over -7