Can you explain to me how exponents work?

Question

asked Oct 20, 2019 16.2k views

2 Answers

SpicyCatGames · Answer 1 · 2019-10-21T18:07:33+0000

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)