Hey! I need help with this question.
Apply the properties of integer exponents to identify all of the expressions equivalent to 18.
a) 2-3
b) 23
c) 123
d) 22x 2-5
e) 2-2x 25
Apply the properties of integer exponents to identify all of the expressions equivalent to 1/8.
a) 2^-3 Is equivalent to 1/8
b) 2^3 Is not equivalent
c) 1
---- This is equivalent to 1/8
2^3
d) 2^2 x 2^-5 Yes it is equivalent to 1/8
e) 2^-2 x 2^5 It is not equivalent to 1/8.
I hope this helped. :-)
confusing question.
18 = 2(3^2) , no such expression in your choices
did you mean 1/8 ??
then 1/8 = 1/2^3 or 2^-3
I see a "2-3" , perhaps ..... ??
notice we show exponents using the ^ key
e.g. 5^3 is "five cubed"
What does it mean by '' explain how your results relate to the properties of integer exponent
Sure! I'd be happy to help you with this question.
To determine which expressions are equivalent to 18, we need to apply the properties of integer exponents.
Let's go through each option and see if it is equivalent to 18:
a) 2^(-3)
To evaluate this expression, we need to remember that a negative exponent signifies a reciprocal. So, 2^(-3) is equivalent to 1/(2^3), which simplifies to 1/8 or 0.125. Therefore, a) 2^(-3) is not equivalent to 18.
b) 2^3
This expression represents 2 raised to the power of 3, which is equal to 2 × 2 × 2 = 8. So, b) 2^3 is not equivalent to 18.
c) 1^23
Any nonzero number raised to the power of zero is equal to 1. Therefore, c) 1^23 is equivalent to 1.
d) 2^2 × 2^(-5)
To simplify this expression, we need to combine the exponents because we are multiplying the same base. So, 2^2 × 2^(-5) can be rewritten as 2^(2 + (-5)), which simplifies to 2^(-3). Using the rule for negative exponents again, we know that 2^(-3) is equal to 1/(2^3), which is equivalent to 1/8 or 0.125. Thus, d) 2^2 × 2^(-5) is not equivalent to 18.
e) 2^(-2) × 2^5
Similar to the previous option, we can combine the exponents because we are multiplying the same base. So, 2^(-2) × 2^5 can be rewritten as 2^(-2 + 5), which simplifies to 2^3. As we determined earlier, 2^3 is equal to 8. Therefore, e) 2^(-2) × 2^5 is not equivalent to 18.
After analyzing all the options, the only expression that is equivalent to 18 is c) 1^23.
I hope this explanation helps you understand how to identify equivalent expressions using the properties of integer exponents. Let me know if you have any further questions!