Simplify this expression using the Quotient Rule of Integer Exponents: t400/t100

Question

a. t300
b. t4
c. 300
d. t500

Answer 1

To simplify the expression \( \frac{t^{400}}{t^{100}} \) using the Quotient Rule of Integer Exponents, you can apply the rule which states:

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

In this case, we have:

\[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300} \]

Thus, the simplified expression is \( t^{300} \).

The correct answer is:

a. \( t^{300} \)

Answer 2

simplify a^67/b^34

a. a^67/b^34
b. a^33
c. 23
d.ab^33

Answer 3

The expression \(\frac{a^{67}}{b^{34}}\) cannot be simplified any further without additional context or instructions. It is already in its simplest form as a fraction involving \(a\) and \(b\).

Thus, the correct answer is:

a. \(\frac{a^{67}}{b^{34}}\)

Answer 4

Apply the Quotient Rule of Integer Exponents to simplify 23^67 divided by 23^32.

a. 1^33
b. 23^33
c. 23^97
d. 97

Answer 5

To simplify the expression \(\frac{23^{67}}{23^{32}}\) using the Quotient Rule of Integer Exponents, which states:

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

we apply it as follows:

\[ \frac{23^{67}}{23^{32}} = 23^{67 - 32} = 23^{35}. \]

It seems there was an oversight as the options do not include \(23^{35}\). None of the provided choices directly reflect the correct simplification of the expression as \(23^{35}\). However, if your options contain a typographical error based on the correct application of exponent rules, please verify the options again.

Hence, the simplified form according to the Quotient Rule is:

\(\mathbf{23^{35}}\) (which is not listed in the provided options).

Answer 6

Apply the Quotient Rule of Integer Exponents to simplify 23^65 divided by 23^32.

a. 1^33
b. 23^33
c. 23^97
d. 97

Answer 7

To simplify the expression \(\frac{23^{65}}{23^{32}}\) using the Quotient Rule of Integer Exponents, we use the formula:

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

Applying this to our expression:

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

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

The correct answer is:

b. \(23^{33}\)

Answer 8

Simplify this expression using the Quotient Rule of Integer Exponents: 12^53 divided by 7^53.

a. 5^53
b. 12^106
c. 5^106
d. 12^53 divided by 7^53

Answer 9

The expression \(\frac{12^{53}}{7^{53}}\) can be simplified by using the properties of exponents.

Using the property that \(\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m\), we can rewrite our expression as follows:

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

However, the expression \(\frac{12^{53}}{7^{53}}\) cannot be simplified to any of the options provided directly in terms of integer exponents.

Therefore, the simplified expression is:

\(\frac{12^{53}}{7^{53}}\), which corresponds to option d.

Answer 10

Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?

a. Check if the bases are the different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.

b. Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as - is otherwise); and write the resulting expression in exponential form.

c. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as - is otherwise); and write the resulting expression in exponential form.

d. Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.

Answer 11

To simplify an exponential expression using the Quotient Rule of Integer Exponents, the correct steps to follow are:

c. Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as - is otherwise); and write the resulting expression in exponential form.

This correctly reflects the Quotient Rule, which states:

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

Thus, the correct response is c.