Respuesta :
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:
[tex]\frac{x^5}{x^3}=x^{(5-3)}=x^2[/tex]
[tex]\frac{x^3}{y^6}[/tex] (can't combine the exponents because they have different bases of x and y)
[tex]\frac{5^3}{5^1} =5^{(3-1)}=5^2=25[/tex]
When you multiply an exponent directly to a fraction or a base with an exponent, you multiply the exponents together for each base.
For example:
[tex](x^4)^2=x^{(4*2)}=x^8[/tex]
[tex](w^2s^3)^5=w^{(2*5)}s^{(3*5)}=w^{10}s^{15}[/tex] (multiply the exponent to each base, w and s)
[tex](\frac{x^3}{y^2})^2=\frac{x^{(3*2)}}{y^{(2*2)}} =\frac{x^6}{y^4}[/tex] (multiply the exponent to each base/top and bottom of the fraction)
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:
[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1} =\frac{1}{x^2}[/tex]
[tex]\frac{1}{2y^{-3}}[/tex] or [tex]\frac{1}{2^1y^{-3}} =\frac{y^3}{2}[/tex]
[tex](\frac{10x^3y^2}{5x^{-3}y^4} )^{-3}[/tex] First simplify the fraction inside the parentheses
[tex](\frac{10}{5} *x^{(3-(-3))}*y^{(2-4)})^{-3}[/tex]
[tex](2*x^6*y^{-2})^{-3}[/tex] Now multiply the exponents by -3
[tex]2^{(1*(-3))}*x^{(6*(-3))}*y^{(-2*(-3))}[/tex]
[tex]2^{-3}x^{-18}y^6[/tex] Make all the exponents positive
[tex]\frac{y^6}{2^3x^{18}}[/tex] Simplify 2³
[tex]\frac{y^6}{8x^{18}}[/tex] [y^6 ÷ 8x^(18)]
Answer:
y^6/8x^18
Step-by-step explanation:
Just got it right on Edge2020.
