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:

`(x^8)/(x^3) =x^(8-3)=x^5`

`(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)=(1)/(x^2)`

`(1)/(x^(-5))=(x^5)/(1) = x^5`

`(y^(-2))/(x^(-1)) =(x^1)/(y^2) =(x)/(y^2)`

1.
`(10^(15))/(10^3) =10^(15-3) = 10^(12)`

2.
`((-3)^4)/((-3)^(-3)) =(-3)^(4-(-3))=(-3)^(4+3) = (-3)^7`

3.
`(8)/(8^3) =8^(1-3) = 8^(-2)=(1)/(8^2)`

4.
`(a^(12))/(a^2) =a^(12-2)=a^(10)`

5.
`(m^(-2)n^(16))/(m^(4)n^2) =(m^(-2-4))(n^(16-2))=(m^(-6))(n^(14))=(n^(14))/(m^(6))`

This is one of the ways you could have done it

6.
`(p^5q^(-10))/(p^6q^(-2)) =(p^(5-6))(q^(-10-(-2)))=(p^(-1))(q^(-8))=(1)/(p^1q^8) =(1)/(pq^8)`

7.
`(63x^(18))/(9x^(2) )` Divide 63 and 9

`(7x^(18))/(x^(2)) =(7)(x^(18-2))=(7)(x^(16))=7x^(16)`

8.
`(28r^4)/(-7r^(15)) =((28)/(-7) )(r^(4-15))=(-4)(r^(-11))=(-4)((1)/(r^(11)) )=(-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`