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

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

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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

User JSoet
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