Question

simplify this expression using the quotient rule of integer exponents 400/100

answers
300
4
300
500

Answer 1

simplify 67/34
answers
a33
ab33
23
a67/b34

Answer 2

apply the quotient rule of integers exponets to simplify 23^65 divided by 23^32

answers
1^33
97
23^97
23^33

Answer 3

To simplify the expression \( \frac{400}{100} \) using the quotient rule of integer exponents, we can recognize that:

\[
400 = 4 \times 100
\]

Thus, we can rewrite the expression:

\[
\frac{400}{100} = \frac{4 \times 100}{100} = 4
\]

Therefore, the simplified result is \( 4 \).

Among the provided answers, the correct choice is **4**.

Answer 4

To simplify the expression \( \frac{67}{34} \), we can observe that both the numerator and the denominator can be divided by their greatest common divisor (GCD).

The GCD of 67 and 34 is 1 (since 67 is a prime number).

Therefore, \( \frac{67}{34} \) cannot be simplified further using integer values, and it remains \( \frac{67}{34} \).

Now, looking at the provided options:

1. **a33**
2. **ab33**
3. **23**
4. **a67/b34**

None of the options directly represent \( \frac{67}{34} \). However, if we interpret \( a \) and \( b \) such that \( a = 67 \) and \( b = 34 \), then option 4, \( \frac{a67}{b34} \), is essentially \( \frac{67}{34} \).

Thus, if we are considering the variable representation, the closest fitting option is:

**a67/b34**.

Answer 5

To simplify the expression \( \frac{23^{65}}{23^{32}} \) using the quotient rule of integer exponents, we apply the principle that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

In this case, we have:

\[
\frac{23^{65}}{23^{32}} = 23^{65 - 32} = 23^{33}
\]

Thus, the simplified form is \( 23^{33} \).

Among the provided answers, the correct choice is:

**23^33**.