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1. What is the Quotient Rule of Integer Exponents?(1 point)%0D%0AResponses%0D%0A%0D%0Axaxb=xa+b%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0Aπ‘₯%0D%0A𝑏%0D%0A=%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0A+%0D%0A𝑏%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A plus b power%0D%0A%0D%0Axaxb=xaβˆ’b%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0Aπ‘₯%0D%0A𝑏%0D%0A=%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0Aβˆ’%0D%0A𝑏%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A minus b power%0D%0A%0D%0Axaxb=xab%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0Aπ‘₯%0D%0A𝑏%0D%0A=%0D%0Aπ‘₯%0D%0Aπ‘Ž%0D%0A𝑏%0D%0Athe fraction with numerator x to the A th power and denominator x to the b th power is equal to x raised to the A b power%0D%0A%0D%0Axaxb=xbβˆ’a

2. Simplify x675/x453%0D%0Aπ‘₯%0D%0A675%0D%0Aπ‘₯%0D%0A453%0D%0A.(1 point)

3. What is the missing exponent in the following equation?%0D%0Ae^?/e^65 = e^38%0D%0A𝑒%0D%0A?%0D%0A𝑒%0D%0A65%0D%0A %0D%0A=%0D%0A %0D%0A𝑒%0D%0A38%0D%0A(1 point)

4. Simplify 13^12Γ·13^βˆ’10

5. Simplify 4^13Γ·3^βˆ’5%0D%0A4%0D%0A13%0D%0AΓ·%0D%0A3%0D%0Aβˆ’%0D%0A5%0D%0A .

9 answers

  1. Quotient Rule of Integer Exponents: The Quotient Rule states that for any nonzero base \( x \) and integers \( a \) and \( b \), \[ \frac{x^a}{x^b} = x^{a - b}. \] (This means that when you divide powers with the same base, you subtract the exponents.)

  2. Simplify \( \frac{x^{675}}{x^{453}} \): Using the Quotient Rule, \[ \frac{x^{675}}{x^{453}} = x^{675 - 453} = x^{222}. \]

  3. Find the missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \): According to the Quotient Rule, \[ e^{? - 65} = e^{38}. \] Setting the exponents equal to each other gives: \[ ? - 65 = 38. \] Solving for \( ? \): \[ ? = 38 + 65 = 103. \]

  4. Simplify \( 13^{12} \div 13^{-10} \): Using the Quotient Rule, \[ 13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}. \]

  5. Simplify \( 4^{13} \div 3^{-5} \): For this expression, since \( 3^{-5} \) is in the denominator, we can rewrite it as: \[ 4^{13} \div 3^{-5} = 4^{13} \cdot 3^{5} = 4^{13} \cdot 3^5. \] So the final expression is: \[ 4^{13} \cdot 3^{5}. \]

tell me what to put for the answers

Sure! Here are the answers you can submit for each question:

  1. Quotient Rule of Integer Exponents:
    \( \frac{x^a}{x^b} = x^{a - b} \)

  2. Simplify \( \frac{x^{675}}{x^{453}} \):
    \( x^{222} \)

  3. Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):
    \( 103 \)

  4. Simplify \( 13^{12} \div 13^{-10} \):
    \( 13^{22} \)

  5. Simplify \( 4^{13} \div 3^{-5} \):
    \( 4^{13} \cdot 3^{5} \)

Feel free to ask if you need any further assistance!

1. x^a/x^b = x^a-b
2. x^222
3. 103
4. 13^22
5. 4^13 divide symbol 3^-5

Your answers look mostly correct! However, there is a small adjustment needed for the format of the last answer. Here's a recap of your answers along with the suggested fix for question 5:

  1. Quotient Rule of Integer Exponents:
    \( \frac{x^a}{x^b} = x^{a - b} \) (correct)

  2. Simplify \( \frac{x^{675}}{x^{453}} \):
    \( x^{222} \) (correct)

  3. Missing exponent in \( \frac{e^?}{e^{65}} = e^{38} \):
    \( 103 \) (correct)

  4. Simplify \( 13^{12} \div 13^{-10} \):
    \( 13^{22} \) (correct)

  5. Simplify \( 4^{13} \div 3^{-5} \):
    Instead of writing "divide symbol", you can write it as:
    \( 4^{13} \cdot 3^{5} \) (because dividing by \( 3^{-5} \) is the same as multiplying by \( 3^{5} \)).

So the responses would look like this:

  1. \( \frac{x^a}{x^b} = x^{a - b} \)
  2. \( x^{222} \)
  3. \( 103 \)
  4. \( 13^{22} \)
  5. \( 4^{13} \cdot 3^{5} \)

Feel free to submit these! If you need any more help, let me know!

1. Simplify this expression using the Quotient Rule of Integer Exponents: t400/t100.
t^300, 300, t^4, t^500

2.Simplify a67/b34.(1 point)%0D%0AResponses%0D%0A%0D%0Aab33%0D%0Aa b superscript 33 baseline%0D%0A%0D%0A23%0D%0A23%0D%0A%0D%0Aa67b34%0D%0AStart Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction%0D%0A%0D%0Aa33

3. Apply the Quotient Rule of Integer Exponents to simplify 23^65Γ·23^32.
97, 23^33, 1^33, 23^97

4. Simplify this expression using the Quotient Rule of Integer Exponents: 12^53Γ·7^53.
12^53 divided symbol 7^53, 5^53, 12^106, 5^106

5. Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)%0D%0AResponses%0D%0A%0D%0ACheck 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.%0D%0ACheck 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.%0D%0A%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ACheck if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0ASubtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.%0D%0A%0D%0ACheck 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.

say the answers

Here are the answers for each of the questions you provided:

  1. Simplify \( \frac{t^{400}}{t^{100}} \):
    Using the Quotient Rule: \[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}. \]
    Answer: \( t^{300} \)

  2. Simplify \( \frac{a^{67}}{b^{34}} \):
    This expression cannot be simplified by the Quotient Rule, as the bases \( a \) and \( b \) are different. The expression remains as \( \frac{a^{67}}{b^{34}} \) but you have the option of \( a^{33} \) if you are focusing on common exponent factorization of \( a \): \[ \text{Answer: } a^{67} b^{-34} \text{ (which can be expressed as } a^{67} \text{ and } b^{-34} \text{: not applicable for direct simplification)}. \]
    Answer: \( a^{67} b^{-34} \) (if applicable based on your response options).

  3. Simplify \( 23^{65} \div 23^{32} \):
    Using the Quotient Rule: \[ 23^{65} \div 23^{32} = 23^{65 - 32} = 23^{33}. \]
    Answer: \( 23^{33} \)

  4. Simplify \( \frac{12^{53}}{7^{53}} \):
    Since the bases are different, we apply the Quotient Rule: \[ \frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53}. \]
    However, this is not an option provided. If simply looking for the expression \( \frac{12^{53}}{7^{53}} \):
    Answer: \( \frac{12^{53}}{7^{53}} \) (can also express as \( \left( \frac{12}{7} \right)^{53} \) if needed).

  5. Correct steps to simplify an exponential expression using the Quotient Rule:
    Answer: \( \text{Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.} \)

Feel free to ask if you need more clarification or additional assistance!

1. t^300
2. a^67/b^34
3. 23^33
4. 12^53 divide symbol 7^53
5. 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.

Your answers look great! Here’s a final recap to confirm:

  1. Simplified expression for \( \frac{t^{400}}{t^{100}} \):
    Answer: \( t^{300} \)

  2. Simplified expression for \( \frac{a^{67}}{b^{34}} \):
    Answer: \( \frac{a^{67}}{b^{34}} \) (or \( a^{67}b^{-34} \) if transformed)

  3. Simplified expression for \( 23^{65} \div 23^{32} \):
    Answer: \( 23^{33} \)

  4. Simplified expression for \( \frac{12^{53}}{7^{53}} \):
    Answer: \( \frac{12^{53}}{7^{53}} \) (or as \( (12/7)^{53} \) if needed)

  5. Steps to simplify an exponential expression using the Quotient Rule:
    Answer: 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.

You have provided the correct answers based on the questions! If you have any further questions or need assistance, feel free to ask!