Question

Can you explain to me how exponents work?

Answer 1

You can't combine exponents when the bases aren't the same.

`x^(2)` "x" is where the base is

For example:

`(x^(2) )(y^4)=x^2y^4` (the bases are x and y)

`(x^3)/(y^7) =(x^3)/(y^7)`

When an exponent is multiplied directly to 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)`

`(2x^(2))^2` You can look at it like this:

`(2^1x^(2) )^2=2^(1(2))x^(2(2)) = 2^2x^4=4x^4`

When a variable with an exponent is multiplied by a variable with an exponent, you add the exponents together.

For example:

`(x^(2) )(x^(3) )=x^(2+3)=x^5`

`(x^3)(x^4)=x^(3+4)=x^7`

`(2x)(x^2)=2x^(1+2)=2x^3`

When an exponent is divided by an exponent, you subtract the exponents.

For example:

`(x^5)/(x^3) =x^(5-3)=x^2`

`(y^4)/(y^1)=y^(4-1)=y^3`

When an exponent is negative, you move the number and its exponent to the other side of the fraction to make the exponent positive.

For example:

`x^(-3)` or
`(x^(-3))/(1)=(1)/(x^3)`

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

`(1)/(y^(-5))=(y^5)/(1)` or
`y^(5)`

Answer 2

1^2 is one squared which means

1x1

1^3 is

1x1x1

2^4 is

2x2x2x2 which equals 16

Explanation: