Recognize and recall powers of 2 up to at least 8192.
A fluency sprint: build the speed and accuracy you need to do this calculation instantly on test day.
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Learn this list until it is automatic. Each value is double the one before it.
Use the exponent rules before you calculate.
Useful links: \(4^2 = 2^4 = 16\), \(8^2 = 2^6 = 64\), \(4^5 = 2^{10} = 1024\), and \(2^{10} \approx 1000\) for estimates.
Common slips: \(2^5 = 10\) (that is \(2 \times 5\)), using the wrong rule (multiplying the exponents when you multiply powers), and adding the powers instead of multiplying them (\(2^3 \times 2^5\) is 256, not \(8 + 32 = 40\)).
With the same base, add the exponents: \(2^{2} \times 2^{4} = 2^{6} = 64\). Multiplying the exponents instead of adding them gives \(256\). Adding the two powers instead of multiplying them gives \(20\). Multiplying the bases too (as \(4^{6}\)) gives \(4096\).
With the same base, multiply the exponents: \((2^{2})^{3} = 2^{6} = 64\). Adding the exponents instead of multiplying them gives \(32\). Multiplying \(2^{2}\) by 3 instead of raising it to the power 3 gives \(12\). Raising the exponent 2 to the power 3 (as \(2^{8}\)) gives \(256\).