document.write( "Question 285143: solve this equation 2x^-1/2=8. is th answer +-2 . thanks \n" ); document.write( "

Algebra.Com's Answer #206993 by jsmallt9(3759) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2x%5E%28-1%2F2%29=8\"$
\n" ); document.write( "We start by isolating the base and its exponent. So we'll get rid of the 2 by dividing both sides by 2:
\n" ); document.write( " $\"x%5E%28-1%2F2%29=4\"$
\n" ); document.write( "From here there are several ways to go. Probably the fastest is base on the idea that we want x to have an exponent of 1. So how can we change an exponent from -1/2 to 1? One way would be to raise both sides of the equation to the -2 power. (You'll see why this works as we do it.)
\n" ); document.write( " $\"%28x%5E%28-1%2F2%29%29%5E%28-2%29=%284%29%5E%28-2%29\"$
\n" ); document.write( "On the left side the rule for the exponents is to multiply them. And what do you get when you multiply -1/2 and -2? Answer: 1! You always get a 1 when you multiply reciprocals! So now we have:
\n" ); document.write( " $\"x+=+%284%29%5E%28-2%29\"$
\n" ); document.write( "Now we just have to simplify the right side:
\n" ); document.write( " $\"x+=+%284%29%5E%28-2%29+=+1%2F%284%5E2%29+=+1%2F16\"$
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