To find which expressions are equivalent to -64, let's evaluate each option step by step:
A. \( 4^{-3} \) \[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad \text{(not -64)} \]
B. \( -(1/4)^{-3} \) \[ -(1/4)^{-3} = -4^3 = -64 \quad \text{(this is -64)} \]
C. \( -2^{-2} \times (2^8) \) \[ -2^{-2} = -\frac{1}{2^2} = -\frac{1}{4} \] \[ -2^{-2} \times (2^8) = -\frac{1}{4} \times 256 = -64 \quad \text{(this is -64)} \]
D. \( 2^3 \times 2^2 \times 2^0 \) \[ 2^3 \times 2^2 \times 2^0 = 2^{3+2+0} = 2^5 = 32 \quad \text{(not -64)} \]
E. \( (2^8) - \frac{2^8}{2^2} \) \[ (2^8) - \frac{2^8}{2^2} = 2^8 - 2^{8-2} = 2^8 - 2^6 = 256 - 64 = 192 \quad \text{(not -64)} \]
After evaluating all the expressions, the two that are equivalent to -64 are:
B. \( -(1/4)^{-3} \)
C. \( -2^{-2} \times (2^8) \)
1 answer