[Note: you can only combine exponents when the base is the same.
x³ "x" is where the base is
For example:
x²(y³) = x²y³
When you multiply a variable/number with an exponent by a number with an exponent, you add the exponents together.
For example:
[tex](x^{2} )(x^{4})=x^{2+4}=x^6[/tex]
[tex](x^{2})(x^6)=x^{2+6}=x^8[/tex]
[tex](2^4)(2^1)=2^{4+1}=2^5[/tex]
When an exponent is negative, you move the number and the exponent to the other side of the fraction to make the exponent positive.
For example:
[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1}=\frac{1}{x^2}[/tex]
[tex]\frac{1}{y^{-3}} =\frac{y^3}{1}[/tex] or y³
A.) [tex]3^{-4}(3^{-3})=3^{-4+(-3)}=3^{-4-3}=3^{-7}=\frac{1}{3^7}[/tex]
B.) [tex]3^{-5}(3^2)=3^{-5+2}=3^{-3}=\frac{1}{3^3}[/tex]
C.) [tex]3^6(3)=3^{6+1}=3^7[/tex]
D.) [tex]3^5(3^{-12})=3^{5+(-12)}=3^{-7}=\frac{1}{3^7}[/tex]
E.) [tex]3^{-7}(3^1)=3^{-7+1}=3^{-6}=\frac{1}{3^6}[/tex]
F.) [tex]3^2(3^{-9}) = 3^{2+(-9)}=3^{-7}=\frac{1}{3^7}[/tex]
Your answer is A, D, F
