Question

Help totally failing need to understand

Answer 1

The reciprocal means total opposite. Meaning you would want to switch the sign of the exponent and the fraction around. 8/7^4

Answer 2

The reciprocal of the base is
`((8)/(7) )^(4)`.

Explanation:

The reciprocal of a number is the multiplicative inverse of that number. What this means is that when the number is multiplied by its reciprocal, you are able to achieve a product of 1.

• ex: The reciprocal of 2 is
  `(1)/(2)`. When we multiply them,
  `(2)/(1) . (1)/(2) = 1`, we get 1.

An exponent has two parts:

1. The base is the number that is being raised.
2. The power is the number the base is being raised by. The power is sometimes also referred to as the exponent.

• ex:
  `10^(2)`. Where 10 is the base that is being raised to the second power.

The exponent laws on negative powers & reciprocals state that:

1. The sign of the exponent is changed.
2. The base is flipped. Meaning if it is a number/integer it is put over 1. If it is already a fraction the numerator and denominator are switched.

• Thus the sign of the exponent is changed from -4 to +4/4.
• And the reciprocal of the base
  `(7)/(8)` is
  `(8)/(7)`.

Thus we get the answer:
`((8)/(7) )^(4)`.

Please let me know if this helped & best of luck!!!