Which of the following is the equivalent expression to Integer Exponents? (1 point) ((15 ^ - 3 * 4 ^ 7) ^ 0)/(4 ^ - 3) that has been generated by applying the Properties of
60/(4 ^ - 3)
1/64
1 * 4 ^ - 3
64
The equivalent expression to ((15 ^ - 3 * 4 ^ 7) ^ 0)/(4 ^ - 3) is 1.
No it’s incorrect
Apologies for the incorrect response. Let's work through the expression step by step:
First, let's simplify the expression inside the parentheses: (15^(-3) * 4^7)^0
Since any number (except for zero) raised to the power of 0 is always equal to 1, we have:
(15^(-3) * 4^7)^0 = 1
So far, the expression simplifies to:
1 / (4^(-3))
Next, let's simplify 4^(-3):
4^(-3) = 1/4^3 = 1/64
Now the expression becomes:
1 / (1/64) = 1 * 64 = 64
Therefore, the equivalent expression is 64.
To find the equivalent expression for ((15 ^ - 3 * 4 ^ 7) ^ 0)/(4 ^ - 3), we can simplify the exponents using the properties of exponents.
First, let's simplify the expression inside the parentheses:
15^-3 * 4^7
Using the property a^-n = 1/a^n and the fact that 15 = 3 * 5:
(1/(3 * 5))^3 * 4^7
(1/3^3 * 5^3) * 4^7
1/3^3 * 5^3 * 4^7
Now, let's simplify the expression in the numerator further by using the property (a*b)^n = a^n * b^n:
(1/3^3 * 5^3 * 4^7)^0
1^0 * (3^3)^0 * (5^3)^0 * (4^7)^0
1 * 1 * 1 * 1
1
So, the expression ((15 ^ - 3 * 4 ^ 7) ^ 0)/(4 ^ - 3) is equivalent to 1.