15^-3•4^7^0/4^-3 which is equivalent? A. 60/4^-3 b. 1/64 c. 64 d.1•4^-3
To solve this problem, we need to simplify the expression.
First, let's consider the exponent rules:
- When we have a negative exponent, it means we have to take the reciprocal of the base raised to the positive exponent. For example, x^-3 is equivalent to 1/x^3.
- When we have a zero exponent, it means the value is equal to 1. For example, x^0 is equal to 1.
Now let's simplify the expression:
15^-3 • 4^7^0 / 4^-3
First, let's simplify 15^-3:
15^-3 = 1/15^3
Next, let's simplify 4^7^0:
4^7^0 = 4^0 = 1
Now, let's simplify 4^-3:
4^-3 = 1/4^3
Substituting these values back into the expression:
1/15^3 • 1 / 1 / 4^3
Simplifying further, remember that dividing by a fraction is equivalent to multiplying by its reciprocal:
1/15^3 • 4^3 / 1
Now, let's simplify the exponent term 15^3:
15^3 = 3375
Substituting the values back into the expression:
1 / 3375 • 4^3 / 1
Now, let's simplify the exponent term 4^3:
4^3 = 64
Substituting the values back into the expression:
1 / 3375 • 64 / 1
Finally, let's multiply the values:
1 • 64 = 64
So, the equivalent expression is 64.
Therefore, the correct option is c) 64.