Which of the following is the equivalent to (15^-3•4^7)^0/4^-3 that has been generated by applying the properties of intiger exponents?
60/4^-3
64
1/64
1•4^-3
To simplify the expression using the properties of integer exponents, we can follow these steps:
First, we apply the power of a product rule, which states that (ab)^n = a^n * b^n. In this case, we have (15^-3 • 4^7)^0, so we can apply the rule to the two bases:
(15^-3)^0 • (4^7)^0
Next, we apply the power of zero rule, which states that any number (except 0) raised to the power of 0 is equal to 1. Therefore, we have:
1 • 1
Finally, we can simplify the expression to just:
1
Therefore, the equivalent expression, generated by applying the properties of integer exponents, is 1.
To simplify the expression (15^-3•4^7)^0/4^-3 using the properties of integer exponents, we can follow these steps:
Step 1: Simplify the exponents:
15^-3 becomes 1/15^3
4^7 stays as it is.
Step 2: Apply the power of a product rule:
(1/15^3•4^7)^0/4^-3 becomes ((1/15^3)•4^7)^0/(4^-3)
Step 3: Apply the power of a quotient rule:
((1/15^3)•4^7)^0/(4^-3) can be rewritten as (4^7/(15^3))^0/(4^-3)
Step 4: Apply the zero exponent rule:
Any nonzero number raised to the power of zero is equal to 1. Therefore, ((4^7/(15^3))^0) is equal to 1.
Step 5: Simplify the expression:
The expression becomes 1/(4^-3).
Step 6: Apply the negative exponent rule:
Any number raised to a negative exponent can be written as the reciprocal of the same number raised to the positive exponent. Therefore, 1/(4^-3) is equal to 1/(1/4^3).
Step 7: Simplify further:
1/(1/4^3) is equal to 1•(4^3/1).
Step 8: Final answer:
Therefore, the equivalent expression is 4^3, which is equal to 64.
Hence, the correct answer is 64.
To determine the equivalent expression to (15^-3 • 4^7)^0 / 4^-3 using the properties of integer exponents, we need to simplify each part of the expression separately and then combine them.
Let's start by simplifying (15^-3 • 4^7)^0:
When any non-zero number is raised to the power of zero, the result is always 1. Therefore, (15^-3 • 4^7)^0 simplifies to 1^0, which is equal to 1.
Now, let's simplify 4^-3:
A negative exponent indicates the reciprocal of the base raised to the positive exponent. So, 4^-3 is equal to 1 / 4^3 or 1 / (4 • 4 • 4), which simplifies to 1 / 64.
Therefore, the expression (15^-3 • 4^7)^0 / 4^-3 simplifies to 1 / 1 / 64, which is equivalent to 1 • 64 or simply 64.
Hence, the answer is 64.