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?

64
1/64
60/4-^3
1 . 4-^3

1 answer

To simplify the expression \((15 - 3 \cdot 4^7)^0 / 4^{-3}\), let's start by breaking it down step by step.

  1. Evaluate \( (15 - 3 \cdot 4^7)^0 \):

    • Any non-zero number raised to the power of 0 is equal to 1. Therefore, \( (15 - 3 \cdot 4^7)^0 = 1 \).
  2. Now, we have: \[ 1 / 4^{-3} \]

  3. Simplifying \( 1 / 4^{-3} \):

    • Using the property of exponents that states \( a^{-n} = \frac{1}{a^n} \), we have: \[ 1 / 4^{-3} = 4^{3} \]
  4. Calculating \( 4^{3} \):

    • \( 4^3 = 64 \).

Through these steps, we find that: \[ \frac{(15 - 3 \cdot 4^7)^0}{4^{-3}} = 64 \]

Therefore, the equivalent expression is 64.