Question

Which of the following expressions have values that are less than the expression below? 6^14 divided by 6^2

6^12*6^-2
(6^3)^3
6^8 divided by 6^-6
6^16*6^-4
6^9 divided by 6^-2

Answer 1

To compare the values of the given expressions, simplify each expression step by step and compare them to the original expression. However, without knowing the values of the variables or the specific operations, it is not possible to determine which expressions are less than the given expression.

Step-by-step explanation:

To compare the values of the given expressions, we need to simplify each expression and then compare them to the original expression. Let's simplify each expression step by step:

1. Expression 1: 6^14 divided by 6^26^12*6^-2(6^3)^36^8 divided by 6^-66^16*6^-46^9 divided by 6^-2
2. Simplify the exponents within parentheses:
   Expression 1: 6^14 divided by 6^26^12*6^-2(6^3)^36^8 divided by 6^-66^16*6^-46^9 divided by 6^-2
   Expression 2: 6^14 divided by 6^26^12*6^-2(6^9)36^8 divided by 6^-66^16*6^-66^9 divided by 6^-2
3. Combine the exponents:
   Expression 1: 6^14 divided by 6^26^12*6^-2(6^9)36^8 divided by 6^-66^16*6^-66^9 divided by 6^-2
   Expression 2: 6^14 divided by 6^26^12*6^-26^936^8 divided by 6^-66^16*6^-66^9 divided by 6^-2
4. Simplify the exponents in each expression:
   Expression 1: 6^14 divided by 6^-17^12*6^-26^936^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
   Expression 2: 6^14 divided by 6^-16^12*6^-26^936^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
5. Simplify the exponents within the parentheses:
   Expression 1: 6^14 divided by 6^-17^12*6^-26^936^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
   Expression 2: 6^14 divided by 6^-16^12*6^-26^16^36^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
6. Simplify the exponents within each expression:
   Expression 1: 6^14 divided by 6^-17^12*6^-26^936^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
   Expression 2: 6^14 divided by 6^-16^8*6^-26^16^36^8 divided by 6^-76^16*6^-76^9 divided by 6^-2

After simplifying the expressions, we have:
Expression 1: 6^14 divided by 6^-17^12*6^-26^936^8 divided by 6^-76^16*6^-76^9 divided by 6^-2
Expression 2: 6^14 divided by 6^-16^8*6^-26^16^36^8 divided by 6^-76^16*6^-76^9 divided by 6^-2

To determine which expressions have values that are less than the given expression, we can simplify the exponents and compare the values of the expressions. However, without knowing the values of the variables or the specific operations, it is not possible to determine which expressions are less than the given expression.