Question

Evaluate the expression. [(3–5)(34)]3 1 Innermost group, apply the product of powers: [3–1]3 2 Apply the power of a power: 3–3 3 Apply the negative exponent: 1 33 4 Simplify: 1 x What is the value of x in the simplified expression?

Answer 1

Answer:

x=27

Step-by-step explanation:

To evaluate the expression: $[(3^{-5})(3^4)]^3$

Step 1:  Innermost group, apply the product of powers ($a^x \times a^y =a^{x+y}$

Therefore:

$(3^{-5})(3^4)=3^{-5+4}=3^{-1}$

We then have:

$=[3^{-1}]^3$

Step 2: Apply the power of a power

$[3^{-1}]^3=3^{-1 \times 3} =3 ^{-3}$

Step 3: Apply the negative exponent

$3 ^{-3} =\dfrac{1}{3^3}$

Step 4: Simplify

$\dfrac{1}{3^3}=\dfrac{1}{27}$

Therefore, the value of x in the simplified expression is 27.