<u>Part a)</u>
Given the expression

Apply exponent rule: 
∵ 
Rewrite 81 as 3 · 27
Rewrite 54 as 2 · 27

Factor out the common term: 27m³n
Therefore,

<u>Part B)</u>
Given the expression

Apply exponent rule: 

Rewrite as

Factor out common term 5y²x²z

Therefore,

Answer:
x=−32/5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
1/2(1/4x−3/5)=1/4(2/5+3/4x)
(1/2)(1/4x)+(1/2)(−3/5)=(1/4)(2/5)+(1/4)(3/4x)(Distribute)(1/2)(1/4x)+(1/2)(−3/5)=(1/4)(2/5)+(1/4)(3/4x)(Distribute)
1/8x+−3/10=1/10+3/16x
1/8x+−3/10=3/16x+1/10
Step 2: Subtract 3/16x from both sides.
1/8x+−3/10−3/16x=3/16x+1/10−3/16x
−1/16x+−3/10=1/10
Step 3: Add 3/10 to both sides.
−1/16x+−3/10+3/10=1/10+3/10
−1/16x=2/5
Step 4: Multiply both sides by 16/(-1).
(16/−1)*(−1/16x)=(16/−1)*(2/5)
x=−3/25