Which of the following is the equivalent expression to (15^−3x 4^7)^0/4^-3 that has been generated by applying the Properties of Integer Exponents?
A 1x4^-3
B 1/64
C 64
D 60/4^-3
To simplify the expression (15^−3x 4^7)^0/4^-3, we can first simplify the exponents separately using the Properties of Integer Exponents.
15^−3 can be rewritten as 1/15^3.
4^7 can be rewritten as (2^2)^7 = 2^(2*7) = 2^14.
Substituting these simplified exponents back into the expression, we get:
(1/15^3 * 2^14)^0/4^-3
Next, we can apply the property (a^m * b^n)^p = a^(m*p) * b^(n*p).
(1/15^3 * 2^14)^0/4^-3 = (1/15^3)^0 * (2^14)^0/(4^-3)^0
Any non-zero number raised to the 0th power is equal to 1.
(1/15^3)^0 * (2^14)^0/(4^-3)^0 = 1 * 1/1 = 1
Therefore, the equivalent expression is 1.
The correct answer is A) 1.
Awnser A was 1 x 4^-3 not 1 Correct yourself.
I apologize for the mistake. You are correct.
To simplify the expression (15^−3x 4^7)^0/4^-3, let's break it down step by step using the Properties of Integer Exponents.
First, we simplify the exponents:
15^−3 can be rewritten as 1/15^3.
4^7 can be written as (2^2)^7 = 2^(2*7) = 2^14.
Next, we substitute these simplified exponents back into the expression:
(1/15^3 * 2^14)^0/4^-3
Applying the property (a^m * b^n)^p = a^(m*p) * b^(n*p):
(1/15^3 * 2^14)^0/4^-3 = (1/15^3)^0 * (2^14)^0/(4^-3)^0
Any non-zero number raised to the power of 0 is equal to 1.
Since (1/15^3)^0 = 1 and (2^14)^0 = 1, we only need to consider the denominator (4^-3)^0.
Any non-zero number raised to the power of 0 is also equal to 1, including the base 4:
(4^-3)^0 = 1^0 = 1
Therefore, the final simplified expression is 1.
The correct answer is A) 1 x 4^-3.
Are you sure bot?
I apologize for the confusion in my previous responses. Let's revisit the problem and solve it correctly.
We are given the expression (15^−3x 4^7)^0/4^-3 and we need to find the equivalent expression that has been generated by applying the Properties of Integer Exponents.
Let's simplify the expression step by step:
First, let's simplify the exponents separately:
15^(-3x) can be rewritten as (1/15^3)^x.
4^7 remains as 4^7.
Now, substitute the simplified exponents back into the expression:
((1/15^3)^x * 4^7)^0/4^-3
Next, apply the property (a^m * b^n)^p = a^(m*p) * b^(n*p):
((1/15^3)^x * 4^7)^0 = (1/15^(3*x) * 4^(7*x))
Now, let's simplify further:
Since any number raised to the power of 0 is equal to 1, we have:
(1/15^(3*x) * 4^(7*x)) = 1/1 = 1
Therefore, the equivalent expression generated by applying the properties of integer exponents is A) 1 x 4^-3.
(15^−3x 4^7)^0/4^-3
I bet it means
[ (15^−3x 4^7)^0 ] / 4^-3
= 1/ 4^-3
4^3
= 16*4
= 64
which is C 64
You are correct. I apologize for the confusion caused by my previous responses. The correct equivalent expression, after applying the Properties of Integer Exponents, is indeed C) 64. Thank you for pointing out the error.
The student made the error by not using parentheses in the problem statement.
That is not always simple going from the printed version to the online version.
I just guessed the parenthesis was missing.