Simplify . (1 point)

Question

a
67
b
34
23
a
67
b
34
a
33
ab
33

Answer 1

To simplify the given expression \( \frac{a^{67} b^{34} 23}{a^{67} b^{34} a^{33} ab^{33}} \), we can start by addressing the numerator and the denominator.

Step 1: Combine like terms in the denominator

Denominator:

1. The term \( a^{67} \) appears first.
2. Then we have \( b^{34} \).
3. The next term is \( a^{33} \), which also contributes to the power of \( a \).
4. Finally, we have \( ab^{33} \), which can be rewritten as \( a^{1} b^{33} \).

Combining the powers of \( a \) in the denominator:

• \( a^{67} \cdot a^{33} \cdot a^{1} = a^{67 + 33 + 1} = a^{101} \)

Combining the powers of \( b \) in the denominator:

• \( b^{34} \cdot b^{33} = b^{34 + 33} = b^{67} \)

So, the denominator simplifies to: \[ a^{101} b^{67} \]

Step 2: Write the simplified form

Now we can rewrite the entire expression: \[ \frac{a^{67} b^{34} 23}{a^{101} b^{67}} \]

Step 3: Simplify the fraction

Next, we can break this down:

1. For \( a \):

   • The powers of \( a \) simplify as follows: \[ \frac{a^{67}}{a^{101}} = a^{67 - 101} = a^{-34} \] This is equivalent to \( \frac{1}{a^{34}} \).

2. For \( b \):

   • The powers of \( b \) simplify as follows: \[ \frac{b^{34}}{b^{67}} = b^{34 - 67} = b^{-33} \] This is equivalent to \( \frac{1}{b^{33}} \).

Step 4: Combine the results

Now we can combine all these components together: \[ \frac{23}{a^{34} b^{33}} \]

Final Result

So the simplified version of the expression is:

\[ \frac{23}{a^{34} b^{33}} \]