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?
Answers
1⋅4^−3
64
60/4^−3
1^64
3 answers
The equivalent expression that has been generated by applying the Properties of Integer Exponents is 1⋅4^−3.
wrong
I apologize for the incorrect response. Let's simplify the expression step by step:
(15^−3 ⋅ 4^7)^0/4^−3
First, we can simplify the exponent of 15^−3:
15^−3 = 1/15^3 = 1/3375
Now we can simplify the expression inside the parentheses:
(1/3375 ⋅ 4^7)^0/4^−3
Next, we simplify the exponent of 4^−3:
4^−3 = 1/4^3 = 1/64
Now we have:
(1/3375 ⋅ 4^7)^0/1/64
Next, we simplify the division of the exponents:
(1/3375 ⋅ 4^7)^0 * 64^1
Any expression raised to the power of zero is equal to 1, so we can simplify further:
1 * 64^1 = 64
Therefore, the equivalent expression is 64.
(15^−3 ⋅ 4^7)^0/4^−3
First, we can simplify the exponent of 15^−3:
15^−3 = 1/15^3 = 1/3375
Now we can simplify the expression inside the parentheses:
(1/3375 ⋅ 4^7)^0/4^−3
Next, we simplify the exponent of 4^−3:
4^−3 = 1/4^3 = 1/64
Now we have:
(1/3375 ⋅ 4^7)^0/1/64
Next, we simplify the division of the exponents:
(1/3375 ⋅ 4^7)^0 * 64^1
Any expression raised to the power of zero is equal to 1, so we can simplify further:
1 * 64^1 = 64
Therefore, the equivalent expression is 64.