Question

Pleases someone explain

Answer 1

When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

$\frac{1}{y^{-2}} =\frac{y^2}{1}$ or $y^2$

$2x^{-3}$ or $\frac{2^1x^{-3}}{1} =\frac{2}{x^3}$

$\frac{1}{x^{-5}} =x^5$

When a base with an exponent is divided by a base with an exponent, you subtract the exponents together. (But you can only combine the exponents when the bases are the same)

For example:

$\frac{x^2}{y}$   (can't combine because they have different bases of y and x)

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

$\frac{2^2}{2} =2^{(2-1)}=2^1 = 2$

When you multiply an exponent directly to a base with an exponent, you multiply the exponents together.

For example:

$(x^2)^3=x^{(2*3)}=x^6$

$(y^2)^{10}=y^{(2*10)}=y^{20}$

$\frac{2e^0}{(e^{-3})^2}$     First multiply the exponents together in the denominator

$\frac{2e^0}{e^{(-3*2)}}= \frac{2e^0}{e^{-6}}$        Now subtract the exponents together

$2e^{(0-(-6))}$  (two negative signs cancel each other out and become positive)

$2e^{(0+6)}$

$2e^6$