Question

Use exponent laws to write each expression with a positive power

Answer 1

`\textsf{(a)} \quad (1)/(3^2)`

`\textsf{(b)} \quad (1)/((-2)^4)`

`\textsf{(c)} \quad 2^2`

Explanation:

Question (a)

`\textsf{Apply the exponent rule:} \quad a^(-n)=(1)/(a^n)`

`\implies 3^(-2)&=(1)/(3^2)`

`\hrulefill`

Question (b)

`\textsf{Apply the exponent rule:} \quad a^(-n)=(1)/(a^n)`

`\implies (-2)^(-4)&=(1)/((-2)^4)`

`\hrulefill`

Question (c)

`\textsf{Apply the exponent rule:} \quad \left((a)/(b)\right)^(-c)=\left((b)/(a)\right)^(c)`

`\implies \left((1)/(2)\right)^(-2)= \left((2)/(1)\right)^(2)`

As 2 / 1 = 2, then:

`\implies \left((1)/(2)\right)^(-2)=2^2`