Question

Please help with only the circled ones (1-8)

Answer 1

When you have an exponent divided by another exponent, you subtract the exponents (only when it has the same base)

For example:

$\frac{x^8}{x^3} =x^{8-3}=x^5$

$\frac{x^3}{x^2} =x^{3-2}=x^{1}$  

When you have a negative exponent, you move it to the other side of the fraction to make the exponent positive

For example:

$x^{-2}=\frac{1}{x^2}$

$\frac{1}{x^{-5}}=\frac{x^5}{1} = x^5$

$\frac{y^{-2}}{x^{-1}} =\frac{x^1}{y^2} =\frac{x}{y^2}$

1. $\frac{10^{15}}{10^3} =10^{15-3} = 10^{12}$

2. $\frac{(-3)^4}{(-3)^{-3}} =(-3)^{4-(-3)}=(-3)^{4+3} = (-3)^7$

3. $\frac{8}{8^3} =8^{1-3} = 8^{-2}=\frac{1}{8^2}$

4. $\frac{a^{12}}{a^2} =a^{12-2}=a^{10}$

5. $\frac{m^{-2}n^{16}}{m^{4}n^2} =(m^{-2-4})(n^{16-2})=(m^{-6})(n^{14})=\frac{n^{14}}{m^{6}}$

This is one of the ways you could have done it

6. $\frac{p^5q^{-10}}{p^6q^{-2}} =(p^{5-6})(q^{-10-(-2)})=(p^{-1})(q^{-8})=\frac{1}{p^1q^8} =\frac{1}{pq^8}$

7. $\frac{63x^{18}}{9x^{2} }$   Divide 63 and 9

$\frac{7x^{18}}{x^{2}} =(7)(x^{18-2})=(7)(x^{16})=7x^{16}$

8. $\frac{28r^4}{-7r^{15}} =(\frac{28}{-7} )(r^{4-15})=(-4)(r^{-11})=(-4)(\frac{1}{r^{11}} )=\frac{-4}{r^{11}}$

[More information with exponents]

If you multiply an exponent directly with another exponent, you multiply the exponents together

For example:

$(x^{2})^4=x^{2(4)}=x^8$

$(x^{3})^5 =x^{3(5)}=x^{15}$

If you multiply a variable with an exponent by a variable with an exponent, you add the exponents

For example:

$(x^{2}) (x^6)=x^{2+6}=x^8$

$(x^{3})(x^1)=x^{3+1}=x^4$