Simplify 13 to the power of 12÷13 to the power of −10

Answer 1

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:

\[ \boxed{13^{22}} \]

Answer 2

simplify 4 to the power of 13÷3 to the power of -5

Answer 3

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:

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

Answer 4

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.

Answer 5

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.