Question

Simplify x raised to the negative seventh power over y raised to the fifth power.

1) -x⁷y⁵
2) 1 / (x⁷y⁵)
3) (y⁵) / (x⁻⁷)
4) (y⁵) / (x⁷)

Answer 1

The expression x raised to the negative seventh power over y raised to the fifth power simplifies to (y^5) / (x^7), because a negative exponent moves the base to the denominator of the fraction.

Step-by-step explanation:

To simplify x raised to the negative seventh power over y raised to the fifth power, remember that a negative exponent indicates that the base should be in the denominator of a fraction. Therefore, x-7 is the same as 1/x7. When you have an expression like x-7/y5, this simplifies to (y5) / (x7) because the negative exponent moves x to the denominator. We keep the positive exponent of y as is, because it is already in the numerator. Thus, the correct answer is option 4) (y5) / (x7).