Tell whether the value of the expression is less than the base of the expression:
a) 2^3
b)(5/6)^3
c) 3^1
d)(5/2)^3
e) 1^3
...b)equals 125/216. So is the correct answer YES it is less than the base?
...d)equals 125/8. Is the correct answer NO it is not less than the base?
if the base is a proper fraction (less than one)
and you are raising it to positive exponents > 1, the answer is less than the base
if the base is a improper fraction (greater than one)
and you are raising it to positive exponents > 1, the answer is greater than the base
b) you are right
d) you are right
e) is the exception, notice the base is neither > nor < than one
1^anything = 1
To determine whether the value of an expression is less than the base of the expression, we need to compare the value of the expression to the value of the base. Let's go through each expression to determine the answer:
a) In the expression 2^3, the base is 2 and the value of the expression is 8. Since 8 is not less than 2, the correct answer is NO, it is not less than the base.
b) In the expression (5/6)^3, the base is 5/6 and the value of the expression is 125/216. To compare these values, we can simplify the division by dividing both the numerator and the denominator by their greatest common divisor. In this case, the greatest common divisor is 1, so the simplified fraction is still 125/216. Since 125/216 is less than 5/6, the correct answer is YES, it is less than the base.
c) In the expression 3^1, the base is 3 and the value of the expression is 3. Since 3 is equal to the base, the correct answer is NO, it is not less than the base.
d) In the expression (5/2)^3, the base is 5/2 and the value of the expression is 125/8. Similar to the previous case, we can simplify the fraction 125/8. By dividing both the numerator and the denominator by their greatest common divisor, which is 1, we get the simplified fraction 125/8. Since 125/8 is not less than 5/2, the correct answer is NO, it is not less than the base.
e) In the expression 1^3, the base is 1 and the value of the expression is 1. Since 1 is equal to the base, the correct answer is NO, it is not less than the base.
I hope this clarifies the answers to the given expressions.