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
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.
To simplify the expression (15^−3 ⋅ 4^7)^0/4^−3 using the Properties of Integer Exponents, we can follow these steps:
Step 1: Apply the exponent property: (a^m)^n = a^(m * n).
(15^−3 ⋅ 4^7)^0 = 15^(−3 * 0) ⋅ 4^(7 * 0) = 15^0 ⋅ 4^0
Step 2: Any number raised to the power of 0 is equal to 1.
15^0 = 1 and 4^0 = 1
Therefore, (15^−3 ⋅ 4^7)^0 = 1 ⋅ 1 = 1
Step 3: Apply the exponent property: a^m / a^n = a^(m - n).
1/4^−3 = 1/4^(0 - (-3)) = 1/4^3
So, the equivalent expression to (15^−3 ⋅ 4^7)^0/4^−3, generated by applying the Properties of Integer Exponents, is 1/4^3, which can also be written as 1/64.
Therefore, the answer is 1/64.
To simplify the given expression using the Properties of Integer Exponents, we can follow these steps:
Step 1: Simplify the exponents inside the parentheses.
(15^−3 ⋅ 4^7) = (1/15^3 ⋅ 4^7) = 1/(15^3) ⋅ (4^7)
Step 2: Simplify the exponent of the denominator.
4^−3 = 1/4^3 = 1/64
Step 3: Substitute the simplified exponents into the expression.
(1/(15^3) ⋅ (4^7))^0/(1/64) = 1/((15^3) ⋅ (4^7))^0/1/64
Step 4: Apply the Property of Exponents: a^0 = 1
1/(1/64) = 1 ⋅ 64 = 64
Therefore, the equivalent expression to (15^−3 ⋅ 4^7)^0/4^−3, generated by applying the Properties of Integer Exponents, is 64.