Which of the following is the equivalent expression to (15^-3•4^7)^0/4^-3 that has been generated by applying the properties of integer exponents
A. 64.
B. 60/4^-3
C. 1 • 4^-3
The equivalent expression can be found by applying the properties of integer exponents.
First, we can simplify the expression inside the parentheses:
(15^-3 • 4^7) = (1/15^3 • 4^7) = (4^7 / 15^3)
Then, we can simplify the exponents by multiplying them:
(4^7 / 15^3) ^ 0 = 4^(7*0) / 15^(3*0) = 4^0 / 15^0
Any non-zero number raised to the power of 0 is equal to 1:
4^0 = 1
15^0 = 1
Therefore, the expression simplifies to:
1 / 1 = 1
The equivalent expression is C. 1 • 4^-3
Which of the following is the equivalent expression to (15^-3•4^7)^0/4^-3 that has been generated by applying the properties of integer exponents
A. 64.
B. 60/4^-3
C. 1 • 4^-3
D. 1/64
To find the equivalent expression, we can simplify the expression inside the parentheses first.
(15^-3 • 4^7) = (1/15^3 • 4^7) = (4^7 / 15^3)
Next, we have a negative exponent on 4^-3. We can rewrite this as the reciprocal with a positive exponent:
4^-3 = 1/4^3
Now we substitute this into the expression:
(4^7 / 15^3) ^ 0 / (1/4^3)
Any number raised to the power of 0 is equal to 1, so the expression becomes:
1 / (1/4^3) = 1 * 4^3 = 4^3 = 64
Therefore, the equivalent expression is A. 64.
What are the following is an equivalent expression to (2^-3•9^3)^-4/2^9•9^-10
Let's simplify the expression step by step.
(2^-3 • 9^3)^-4 / (2^9 • 9^-10)
First, let's simplify the expressions inside the parentheses:
2^-3 = 1 / 2^3 = 1/8
9^3 = 9 * 9 * 9 = 729
So, the expression becomes:
(1/8 • 729)^-4 / (2^9 • 9^-10)
Next, let's simplify the exponents:
(1/8)^-4 = (8^1)^4 = 8^4 = 4096
(9^-10) = 1/(9^10)
Now, the expression becomes:
4096 / (2^9 • 1/(9^10))
Simplifying further:
2^9 = 512
So, the expression is:
4096 / (512 • 1/(9^10))
Multiplying 512 and the reciprocal of 9^10:
4096 / (512/9^10)
Multiplying 4096 and 9^10:
(4096 • 9^10) / 512
Now, let's simplify the expression further if possible.
There are no common factors between 4096 and 512, so let's prime factorize them:
4096 = 2^12
512 = 2^9
So, the expression becomes:
(2^12 • 9^10) / (2^9)
Now, dividing the exponents:
2^12 / 2^9 = 2^(12-9) = 2^3 = 8
Therefore, the equivalent expression is:
(2^12 • 9^10) / (2^9) = 8 • (9^10) = 8 • 3486784401 = 27,938,907,208.
So the equivalent expression is just a numerical value and does not match any of the options given.
What are the following is an equivalent expression to (2^-3•9^3)^-4/2^9•9^-10
A. 2^3/9^2
B. 2^3 • 9^2
C. 2^12•9^-12/2^9•9^-10
D. 2^-7•9^-10/2^9•9^-10
To find the equivalent expression, let's simplify the given expression step by step.
Starting with (2^-3 • 9^3)^-4/2^9 • 9^-10:
First, let's simplify the expressions inside the parentheses:
2^-3 = 1 / 2^3 = 1/8
9^3 = 9 * 9 * 9 = 729
So, the expression becomes: (1/8 • 729)^-4/2^9 • 9^-10
Next, let's simplify the exponents:
(1/8)^-4 = (8^1)^4 = 8^4 = 4096
(9^-10) = 1/(9^10)
Now, the expression becomes: 4096/2^9 • 1/(9^10)
Now, let's simplify the remaining exponents:
2^9 = 512
9^10 = 3486784401
So, the expression becomes: 4096/512 • 1/(3486784401)
Simplifying further:
4096/512 = 8
So, the expression becomes: 8 • 1/(3486784401)
Multiplying 8 and the reciprocal of 3486784401:
8 • 1/(3486784401) = 8/(3486784401)
Therefore, the equivalent expression is option D. 2^-7 • 9^-10 / 2^9 • 9^-10.
Note that the 9^-10 term cancels out from the numerator and denominator, leaving us with 2^-7/2^9. Simplifying the exponents further, we have 2^(-7-9) = 2^-16.