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
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.
\[
\frac{x^a}{x^b} = x^{a-b}
\]
So, the first option is the correct representation of the Quotient Rule.
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:
\[
\frac{x^{675}}{x^{453}} = x^{222}
\]
\[
\frac{x^a}{x^b} = x^{a-b}
\]
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
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 \(103\).
\[
\frac{e^{?}}{e^{65}} = e^{38},
\]
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
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:
\[
\frac{13^{12}}{13^{-10}} = 13^{22}.
\]
\[
\frac{x^a}{x^b} = x^{a-b}.
\]
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
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:
\[
4^{13} \cdot 3^{5}.
\]
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}.
\]
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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