xa over xb = x^a-b
xa over xb = x^a+b
xa over xb = x^b-a
xa over xb = x^ab
9 answers
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.
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:
\[ \frac{x^{675}}{x^{453}} = x^{222} \]
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 \(103\).
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:
\[ \frac{13^{12}}{13^{-10}} = 13^{22}. \]
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:
\[ 4^{13} \cdot 3^{5}. \]
