Asked by yayy

What is the Quotient Rule of Integer Exponents?
xa over xb = x^a-b
xa over xb = x^a+b
xa over xb = x^b-a
xa over xb = x^ab

Answers

Answered by GPT-4o mini
The Quotient Rule of Integer Exponents states that when you divide two exponential expressions with the same base, you subtract the exponents. The correct expression is:

\[
\frac{x^a}{x^b} = x^{a-b}
\]

So, the first option is the correct representation of the Quotient Rule.
Answered by yayy
Simplify x^675 over x^453.
Answered by GPT-4o mini
To simplify the expression \(\frac{x^{675}}{x^{453}}\), you can apply the Quotient Rule of Integer Exponents, which states that:

\[
\frac{x^a}{x^b} = x^{a-b}
\]

In this case, \(a = 675\) and \(b = 453\). So, we have:

\[
\frac{x^{675}}{x^{453}} = x^{675 - 453}
\]

Now, calculate \(675 - 453\):

\[
675 - 453 = 222
\]

Therefore, the simplified expression is:

\[
\frac{x^{675}}{x^{453}} = x^{222}
\]
Answered by yayy
What is the missing exponent in the following equation? e^? over e^65 = e^38
Answered by GPT-4o mini
To find the missing exponent in the equation

\[
\frac{e^{?}}{e^{65}} = e^{38},
\]

you can use the Quotient Rule of Exponents, which states:

\[
\frac{e^a}{e^b} = e^{a-b}.
\]

Applying this rule, we can rewrite the left side of the equation:

\[
e^{? - 65} = e^{38}.
\]

Since the bases are the same (both are \(e\)), we can set the exponents equal to each other:

\[
? - 65 = 38.
\]

To solve for the missing exponent \(?\), add 65 to both sides:

\[
? = 38 + 65.
\]

Calculating the right side:

\[
? = 103.
\]

Therefore, the missing exponent is \(103\).
Answered by yayy
Simplify 13^12 divided by 13^-10.
Answered by GPT-4o mini
To simplify the expression \(\frac{13^{12}}{13^{-10}}\), you can apply the Quotient Rule of Exponents, which states:

\[
\frac{x^a}{x^b} = x^{a-b}.
\]

In this case, let \(a = 12\) and \(b = -10\). Thus, we have:

\[
\frac{13^{12}}{13^{-10}} = 13^{12 - (-10)}.
\]

This simplifies to:

\[
13^{12 + 10} = 13^{22}.
\]

Therefore, the simplified expression is:

\[
\frac{13^{12}}{13^{-10}} = 13^{22}.
\]
Answered by yayy
Simplify 4^13 divided by 3^-5.
Answered by GPT-4o mini
To simplify the expression \(\frac{4^{13}}{3^{-5}}\), you can approach it by recalling that dividing by a negative exponent is equivalent to multiplying by the positive exponent:

\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}.
\]

This gives you the final expression:

\[
4^{13} \cdot 3^5.
\]

Since these two terms are multiplication of different bases, \(4^{13}\) and \(3^{5}\) cannot be simplified further as a single term. Thus, the simplified expression is:

\[
4^{13} \cdot 3^{5}.
\]

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