Respuesta :
Recall that the product rule of exponents is given by
[tex]a^x\cdot a^y=a^{x+y}[/tex]Recall that the quotient rule of exponents is given by
[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]Recall that the negative rule of exponents is given
Expression 1:
Let us apply the product rule of exponents to the expression
[tex]2^{-2}\cdot2^{-2}=2^{-2+(-2)}=2^{-2-2}=2^{-4}[/tex]Now let us apply the negative rule of exponents to the above expression
[tex]2^{-4}=\frac{1}{2^4}[/tex]Therefore, the 1st expression matches with the 5th answer.
Expression 2:
Let us apply the product rule of exponents to the expression
[tex]2^{-2}\cdot2^2=2^{-2+2}=2^0=1[/tex]Please note that any number having an exponent of 0 is equal to 1
Therefore, the 2nd expression matches with the 3rd answer
Expression 3:
Let us apply the product rule of exponents to the expression
[tex]2^4\cdot2^{-5}=2^{4+(-5)}=2^{4-5}=2^{-1}[/tex]Now let us apply the negative rule of exponents to the above expression
[tex]2^{-1}=\frac{1}{2}[/tex]Therefore, the 3rd expression matches with the 2nd answer.
Expression 4:
Let us apply the quotient rule of exponents to the expression
[tex]\frac{2^8}{2^2}=2^{8-2}=2^6[/tex]Therefore, the 4th expression matches with the 6th answer.
Expression 5:
Let us apply the quotient rule of exponents to the expression
[tex]\frac{2^3}{2^{12}}=2^{3-12}=2^{-9}[/tex]Now let us apply the negative rule of exponents to the above expression
[tex]2^{-9}=\frac{1}{2^9}[/tex]Therefore, the 5th expression matches with the 1st answer.
Expression 6:
Let us apply the quotient rule of exponents to the expression
[tex]\frac{2^{10}}{2^6}=2^{10-6}=2^4[/tex]Therefore, the 6th expression matches with the 4th answer.
