What is the decimal value of 2 raised to the power of -3?

What is the decimal value of 2 raised to the power of -3?

• A. 0.25
• B. 0.5
• C. 0.125
• D. 0.75

Answer: (C)

To find the decimal value of \(2\) raised to the power of \(-3\), we can use the rule that states any number raised to a negative exponent is equivalent to the reciprocal of that number raised to the positive exponent. Therefore, \(2^{-3}\) can be rewritten as \(\frac{1}{2^{3}}\). Next, we calculate \(2^{3}\): \[ 2^{3} = 2 \times 2 \times 2 = 8 \] So, \(2^{-3}\) becomes: \[ 2^{-3} = \frac{1}{2^{3}} = \frac{1}{8} \] To convert \(\frac{1}{8}\) into decimal form, we divide \(1\) by \(8\): \[ 1 \div 8 = 0.125 \] Thus, the decimal value of \(2^{-3}\) is \(0.125\), which corresponds to the choice indicating this value.

To find the decimal value of (2) raised to the power of (-3), we can use the rule that states any number raised to a negative exponent is equivalent to the reciprocal of that number raised to the positive exponent. Therefore, (2^{-3}) can be rewritten as (\frac{1}{2^{3}}).

Next, we calculate (2^{3}):

[

2^{3} = 2 \times 2 \times 2 = 8

]

So, (2^{-3}) becomes:

[

2^{-3} = \frac{1}{2^{3}} = \frac{1}{8}

]

To convert (\frac{1}{8}) into decimal form, we divide (1) by (8):

[

1 \div 8 = 0.125

]

Thus, the decimal value of (2^{-3}) is (0.125), which corresponds to the choice indicating this value.