When you have an exponent divided by another exponent, you subtract the exponents (only when it has the same base)
For example:
[tex]\frac{x^8}{x^3} =x^{8-3}=x^5[/tex]
[tex]\frac{x^3}{x^2} =x^{3-2}=x^{1}[/tex]
When you have a negative exponent, you move it to the other side of the fraction to make the exponent positive
For example:
[tex]x^{-2}=\frac{1}{x^2}[/tex]
[tex]\frac{1}{x^{-5}}=\frac{x^5}{1} = x^5[/tex]
[tex]\frac{y^{-2}}{x^{-1}} =\frac{x^1}{y^2} =\frac{x}{y^2}[/tex]
1. [tex]\frac{10^{15}}{10^3} =10^{15-3} = 10^{12}[/tex]
2. [tex]\frac{(-3)^4}{(-3)^{-3}} =(-3)^{4-(-3)}=(-3)^{4+3} = (-3)^7[/tex]
3. [tex]\frac{8}{8^3} =8^{1-3} = 8^{-2}=\frac{1}{8^2}[/tex]
4. [tex]\frac{a^{12}}{a^2} =a^{12-2}=a^{10}[/tex]
5. [tex]\frac{m^{-2}n^{16}}{m^{4}n^2} =(m^{-2-4})(n^{16-2})=(m^{-6})(n^{14})=\frac{n^{14}}{m^{6}}[/tex]
This is one of the ways you could have done it
6. [tex]\frac{p^5q^{-10}}{p^6q^{-2}} =(p^{5-6})(q^{-10-(-2)})=(p^{-1})(q^{-8})=\frac{1}{p^1q^8} =\frac{1}{pq^8}[/tex]
7. [tex]\frac{63x^{18}}{9x^{2} }[/tex] Divide 63 and 9
[tex]\frac{7x^{18}}{x^{2}} =(7)(x^{18-2})=(7)(x^{16})=7x^{16}[/tex]
8. [tex]\frac{28r^4}{-7r^{15}} =(\frac{28}{-7} )(r^{4-15})=(-4)(r^{-11})=(-4)(\frac{1}{r^{11}} )=\frac{-4}{r^{11}}[/tex]
[More information with exponents]
If you multiply an exponent directly with another exponent, you multiply the exponents together
For example:
[tex](x^{2})^4=x^{2(4)}=x^8[/tex]
[tex](x^{3})^5 =x^{3(5)}=x^{15}[/tex]
If you multiply a variable with an exponent by a variable with an exponent, you add the exponents
For example:
[tex](x^{2}) (x^6)=x^{2+6}=x^8[/tex]
[tex](x^{3})(x^1)=x^{3+1}=x^4[/tex]
