Asked by Yuji Itadori ^u^
Simplify 13 to the power of 12÷13 to the power of −10
Answers
Answered by
Yuji Itadori ^u^
simplify 4 to the power of 13÷3 to the power of -5
Answered by
Yuji Itadori ^u^
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
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.
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.
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.
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.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Responses
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.
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.
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.
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.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Answered by
GPT-4o mini
To simplify \( 13^{12} \div 13^{-10} \), you can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, let \( a = 13 \), \( m = 12 \), and \( n = -10 \). Thus, we have:
\[
13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}
\]
So, the simplified expression is:
\[
\boxed{13^{22}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, let \( a = 13 \), \( m = 12 \), and \( n = -10 \). Thus, we have:
\[
13^{12} \div 13^{-10} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}
\]
So, the simplified expression is:
\[
\boxed{13^{22}}
\]
Answered by
GPT-4o mini
To simplify the expression \( \frac{4^{13}}{3^{-5}} \), we can reorganize the expression by applying the property of negative exponents, which states that \( \frac{1}{a^{-n}} = a^n \).
Thus, we have:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
This means we multiply \( 4^{13} \) by \( 3^{5} \):
\[
4^{13} \cdot 3^{5}
\]
Since this is a multiplication of different bases, it can't be simplified further in terms of combining terms. Therefore, the simplified expression is:
\[
\boxed{4^{13} \cdot 3^{5}}
\]
Thus, we have:
\[
\frac{4^{13}}{3^{-5}} = 4^{13} \cdot 3^{5}
\]
This means we multiply \( 4^{13} \) by \( 3^{5} \):
\[
4^{13} \cdot 3^{5}
\]
Since this is a multiplication of different bases, it can't be simplified further in terms of combining terms. Therefore, the simplified expression is:
\[
\boxed{4^{13} \cdot 3^{5}}
\]
Answered by
GPT-4o mini
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
**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.**
So, the first option you provided is the correct one:
**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.**
**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.**
So, the first option you provided is the correct one:
**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.**