Question

Can you explain to me how exponents work?

Answer 1

Answer:

1^2 is one squared which means

1x1

1^3 is

1x1x1

2^4 is

2x2x2x2 which equals 16

Step-by-step explanation:

Answer 2

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)

$\frac{x^3}{y^7} =\frac{x^3}{y^7}$

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:

$\frac{x^5}{x^3} =x^{5-3}=x^2$

$\frac{y^4}{y^1}=y^{4-1}=y^3$

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 $\frac{x^{-3}}{1}=\frac{1}{x^3}$

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

$\frac{1}{y^{-5}}=\frac{y^5}{1}$ or $y^{5}$