Question

What is the quotient?
7^-6/7^2
1/7^8
1/7^3
7^3
7^8

Answer 1

To calculate the quotient of powers with the same base, subtract the exponents in the denominator from those in the numerator. The given expression simplifies to 7^-94, applying the rules of exponents.

Step-by-step explanation:

To find the quotient of powers, we apply the rules of exponents. For division, we subtract the exponents when the bases are the same, and we divide the coefficients separately. Using the given expression, let's calculate the quotient:

• First, write the expression with positive exponents: 7-6 ÷ 721 ÷ 781 ÷ 737 × 737 × 78.
• Apply the quotient rule for exponents: am ÷ an = am-n.
• Combine the exponents by summing those that are in the numerator and subtracting those that are in the denominator: 7(-6) + 37 + 8 - (21 + 81 + 37) = 7-94.

Thus, the final quotient is 7-94.