Answer:
x=27
Step-by-step explanation:
To evaluate the expression: [tex][(3^{-5})(3^4)]^3[/tex]
Step 1: Innermost group, apply the product of powers ([tex]a^x \times a^y =a^{x+y}[/tex]
Therefore:
[tex](3^{-5})(3^4)=3^{-5+4}=3^{-1}[/tex]
We then have:
[tex]=[3^{-1}]^3[/tex]
Step 2: Apply the power of a power
[tex][3^{-1}]^3=3^{-1 \times 3} =3 ^{-3}[/tex]
Step 3: Apply the negative exponent
[tex]3 ^{-3} =\dfrac{1}{3^3}[/tex]
Step 4: Simplify
[tex]\dfrac{1}{3^3}=\dfrac{1}{27}[/tex]
Therefore, the value of x in the simplified expression is 27.
