To simplify the given expression using the properties of integer exponents, we can start by dividing the exponents:
(15^(-3) x 4^7)^(0) / 4^(-3)
Anything raised to the power of 0 is equal to 1:
1 / 4^(-3)
Since a negative exponent indicates the reciprocal, we can rewrite 4^(-3) as 1/4^3:
1 / (1/4^3)
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:
1 * (4^3/1)
This simplifies to:
4^3
Using the property that a number raised to a power is equal to multiplying the number by itself that many times, 4^3 is equal to 4 * 4 * 4, which is equal to 64.
Therefore, the equivalent expression is 64.
The answer is C: 64.
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: 1 X 4^-3
C: 64
D: 60/4^-3
1 answer