<p>I'm trying to practice for the SAT and using my calc may take some time. So I want to know how to do some problems directly in my head.</p>
<p>16^−3 / 4</p>
<p>Basically its 16 to the -3/4</p>
<p>So to start, we know that the negative exponent means we need to flip it to the bottom. So now we have:
1/((16)^(3/4))</p>
<p>With the 3/4 exponent, it’s always “power over root”. We can first take the 4th root of 16, which is 2.</p>
<p>Then, because the 3 is still there in the exponent, we need to raise 2 to the 3rd power.
2^3=8</p>
<p>That 8 is in the bottom of the rational expression, so the final answer is</p>
<p>1/8</p>
<p>It’s probably to your advantage to use your calc. Under pressure during the SAT you’re apt to make silly mistakes. It’s safer and quicker to use a calc, IMO.</p>
<p>Actually for this question it takes longer to use a calculator. IdFactor basically explained it pretty good…negative means you take the reciprocal of the number (because remember functions…f^-1 means the reciprocal function), top number makes it bigger so it is the power, and bottom number makes it smaller so it is the root thingy…</p>
<p>so 16^(-3/4) equals 1/(4throot(16))^3 = 1/(2)^3 = 1/8.</p>
<p>I’m going with JNE23. It’s not worth doing it in your hand. Just hit the calculator.</p>
<p>Just make sure you type it in right… </p>
<p>16 ^ (-3/4)</p>
<p>Or you can even do -3/4 and then do 16 ^ ANS</p>
<p>Calculator FTW!</p>
<p>yeah, the time it takes me to press 9 keys on a calculator is far quicker than it takes for me to recall exponent properties and find the fourth route of 16 cubed.</p>
<p>Either way this question shouldn’t take more than 30 seconds, so its not that big of an issue…but still…calc wins.</p>
<p>It’s a pretty simple question. Exponents and their functions make up a very easy topic I think. You’ll be fine as long as you know all the laws.</p>
<p>Well for me it takes way longer to do the question with a calculator…</p>
<p>I would use the calculator just in case I made a mistake. But it also takes longer for me to do it with a calculator.</p>
<p>You may need to manipulate an exponential statement like this on the SAT, but you will not need to simply find its value. </p>
<p>These are they basic things the College Board will reward you for knowing about this: </p>
<ol>
<li><p>that 16 ^ (-3/4) is actually 1 / 16 ^(3/4) [knowing that the negative exponent means reciprocal is always important on the SAT]</p></li>
<li><p>you can “isolate” the 16 by raising this value (and whatever is on the other side of the equation) to (-4/3), which will cause your exponents to cancel</p></li>
</ol>
<p>99% of problems that would include this on the SAT will be checking to see if you know those to facts. </p>
<p>~cheers!</p>