Respuesta :
Part (1) : The solution is [tex]729[/tex]
Part (2): The solution is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The solution is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Explanation:
Part (1): The expression is [tex]3^{2} \cdot3^{4}[/tex]
Applying the exponent rule, [tex]$a^{b} \cdot a^{c}=a^{b+c}$[/tex], we get,
[tex]$3^{2} \cdot 3^{4}=3^{2+4}$[/tex]
Adding the exponent, we get,
[tex]3^{2} \cdot3^{4}=3^6=729[/tex]
Thus, the simplified value of the expression is [tex]729[/tex]
Part (2): The expression is [tex]$\left(2 x^{2}\right)^{-4}$[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$[/tex]
Simplifying the expression, we have,
[tex]\frac{1}{2^4x^8}[/tex]
Thus, we have,
[tex]$\frac{1}{16 x^{8}}$[/tex]
Thus, the value of the expression is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The expression is [tex]$\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$[/tex]
Applying the exponent rule, [tex]$\frac{x^{a}}{x^{b}}=x^{a-b}$[/tex], we have,
[tex]\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}[/tex]
Adding the powers, we get,
[tex]\frac{2x^{2}y^{-1}z^{-7}}{3}[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Thus, the value of the expression is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
