<p>how does one do a number such as 0.8 ^6 without using a calculator. I need to find the efficiency and I have no idea how one could do that without a calculator. Am I missing something?</p>
<p>.8 * .8 * .8 * .8 * .8 * .8 …</p>
<p>Or use your powers:
8^2 = 64
8^3 = 512 (so .8^3 = .512)</p>
<p>Then you only have to do .512 * .512</p>
<p>Oh my lol… I thought there was some trick I was missing… Thanks you very much~
this will be a pain the butt to do on the ap exam -_-</p>
<p>Thank baby jesus I finished APES last year and got a 5. 'Twas fun self-studying it though.</p>
<p>0.8^6 = (4/5)^6 = 4^6/5^6 = 2^12/5^6</p>
<p>if you aren’t comfortable with decimals, change it to an integer or fraction. For example, .8= (8)(10^-1). Also, check numbers for perfect squares or perfect cubes. 8=2^3. </p>
<p>.8^6= (8^6)(10^-1)^6= (2^3)^6(10^-6)=(2^18)(10^-6). If you know your powers of 2, or just calculate it on spot-it’s easy- than you have (262144)(10^-6)= .262144</p>
<p>A little off topic, but the following was on the Harvard 1869 entrance exam:</p>
<p>“Find the cube root of 0.0093 to five places of decimals.”</p>
<p>Try that without a calculator.</p>