Question

simplify this expression using the quotient rule of integer exponent: 12^53 / 7^53

Answer 1

simplify this expression using the quotient rule of integer exponent: 12^53 / 7^53
A)5^106
B)5^53
C)12^53/7^53
D)12^106

Answer 2

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the quotient rule of integer exponents, we can apply the rule that states:

\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]

In your case, we can set \( a = 12 \), \( b = 7 \), and \( m = 53 \).

Applying the rule, we get:

\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]

So the simplified expression is:

\[
\left(\frac{12}{7}\right)^{53}
\]

Answer 3

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the quotient rule of integer exponents, we have:

\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]

However, this does not directly match any of the provided options. Let's take a closer look:

The options given are:
A) \( 5^{106} \)
B) \( 5^{53} \)
C) \( \frac{12^{53}}{7^{53}} \)
D) \( 12^{106} \)

Since we derived that \( \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \), we can conclude that the expression simplifies to itself. Therefore, the correct option is:

**C) \( \frac{12^{53}}{7^{53}} \)**