Which expression is equivalent to -64? (1 point)

Question

Responses

23⋅22⋅20
2 cubed times 2 squared times 2 to the 0 power

4−3
4 to the negative 3 power

−2−2⋅(28)
negative 2 to the negative 2 power times open paren 2 to the 8th power close paren
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Answer 1

To find the equivalent expression for \(-64\), let's evaluate each of the given options:

1. \(2^3 \cdot 2^2 \cdot 2^0\):

   • Calculate this expression:
     • \(2^3 = 8\)
     • \(2^2 = 4\)
     • \(2^0 = 1\)
   • Combine them:
     • \(8 \cdot 4 \cdot 1 = 32\)
   • So, this expression is \(32\), not \(-64\).

2. \(4^{-3}\):

   • Rewrite this using the property of exponents:
     • \(4^{-3} = \frac{1}{4^3} = \frac{1}{64}\)
   • So, this expression is \(0.015625\), not \(-64\).

3. \(-2^{-2} \cdot (2^8)\):

   • Calculate \(-2^{-2}\):
     • \(-2^{-2} = -\frac{1}{2^2} = -\frac{1}{4}\)
   • Calculate \(2^8\):
     • \(2^8 = 256\)
   • Now multiply:
     • \(-\frac{1}{4} \cdot 256 = -64\)

Thus, the expression that is equivalent to \(-64\) is \(-2^{-2} \cdot (2^8)\).