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asked Aug 23, 2021 72.7k views

1 Answer

Emilia Bopp · Answer 1 · 2021-08-29T15:04:44+0000

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

For example:

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

(1)/(y^(-2)) =(y^2)/(1) or
y^2

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

For example:

(x^3)^2=x^((3*2))=x^6

$(x^{(1)/(2)} )^{(3)/(2) }=x^{((1)/(2) *(3)/(2) )}=x^{(3)/(4) }$

When you multiply an exponent directly to a fraction, you multiply the exponent to the top and bottom of the fraction.

For example:

((x)/(y) )^2 or
((x^1)/(y^1) )^2=(x^((1*2)))/(y^((1*2))) =(x^2)/(y^2)

$(y^2*z^{-(1)/(4)})^{(5)/(2) }$ First make all of the exponents positive

$(\frac{y^2}{z^{(1)/(4)} } )^{(5)/(2) }$ Now multiply the exponent into the fraction

$\frac{y^{(2*(5)/(2))} }{z^{((1)/(4)*(5)/(2) )} } =\frac{y^5}{z^{(5)/(8) } }$ [y^(5) ÷ z^(5/8)]