which of the following is The equivalent expression to (15^-3 x 4^7)^0 / 4^-3 that has been generated by applying the Properties of Integer Exponents?
a. 1/64
b. 64
c. 60/4^-3
d. 1 x 4^-3
To simplify this expression, let's apply the properties of integer exponents.
First, let's simplify the expression inside the parentheses:
(15^-3 x 4^7) = (1/15^3 x 4^7) = (1/3375 x 16384)
Now, let's simplify the expression outside the parentheses:
(1/3375 x 16384)^0 = 1
Finally, let's simplify the expression with the negative exponent:
4^-3 = 1/4^3 = 1/64
Putting it all together:
(15^-3 x 4^7)^0 / 4^-3 = 1/1 / 1/64 = 64
Therefore, the equivalent expression is option b. 64.
To find the equivalent expression, let's break down the given expression and apply the properties of integer exponents.
First, let's simplify (15^-3 x 4^7)^0. Any number raised to the power of zero is always equal to 1. Therefore, (15^-3 x 4^7)^0 simplifies to 1.
Next, let's simplify 4^-3. When a negative exponent is used, the base is moved to the denominator and the exponent becomes positive. So, 4^-3 becomes 1/4^3.
Putting it all together, the given expression (15^-3 x 4^7)^0 / 4^-3 simplifies to 1 / 1/4^3.
To divide by a fraction, we can multiply by its reciprocal. So, 1 / 1/4^3 is the same as 1 x 4^3.
Therefore, the equivalent expression generated by applying the properties of integer exponents is d. 1 x 4^-3.