Fill in the blanks!

Question

Simplify these expressions that have a variable base.

m^(5) n^(-2)
m^(5) n^(-2) = (m^(5)) (n^(-2))
=(m^(5) 1/n^(_)
=m^(_)/n^(2)

j^(-6) p^(-9)
j^(-6) p^(-9) = (j^(-6)(p^(-9)
=(1/j^(_)) (1/p^(_))
=1/j^(6) p^(_)

Answer 1

Let's fill in the blanks for the given expressions.

1. For the expression \( m^{(5)} n^{(-2)} \): \[ m^{(5)} n^{(-2)} = (m^{(5)}) (n^{(-2)}) \ = (m^{(5)} \cdot \frac{1}{n^{(2)}}) \ = \frac{m^{(5)}}{n^{(2)}} \] Therefore, the blanks are: \( m^{(5)} n^{(-2)} = (m^{(5)}) (n^{(-2)}) = (m^{(5)} \cdot \frac{1}{n^{(2)}}) = \frac{m^{(5)}}{n^{(2)}} \).

2. For the expression \( j^{(-6)} p^{(-9)} \): \[ j^{(-6)} p^{(-9)} = (j^{(-6)})(p^{(-9)}) \ = \left(\frac{1}{j^{(6)}}\right) \left(\frac{1}{p^{(9)}}\right) \ = \frac{1}{j^{(6)} p^{(9)}} \] Therefore, the blanks are: \( j^{(-6)} p^{(-9)} = (j^{(-6)}(p^{(-9)}) = \left(\frac{1}{j^{(6)}}\right) \left(\frac{1}{p^{(9)}}\right) = \frac{1}{j^{(6)} p^{(9)}} \).

So the completed expressions are:

1. \( m^{(5)} n^{(-2)} = (m^{(5)}) (n^{(-2)}) = (m^{(5)} \cdot \frac{1}{n^{(2)}}) = \frac{m^{(5)}}{n^{(2)}} \)

2. \( j^{(-6)} p^{(-9)} = (j^{(-6)})(p^{(-9)}) = \left(\frac{1}{j^{(6)}}\right) \left(\frac{1}{p^{(9)}}\right) = \frac{1}{j^{(6)} p^{(9)}} \)