Asked by mota
A STUDENT SAID THAT 3^5 / 9^5 IS THE SAME AS 1/3 . WHAT MISTAKE HAS THE STUDENT MADE ?
Answers
Answered by
mota
MY ANSWER IS
THEY SUBTRACT THE EXPONENT AND THEN THEY SIMPLIFY THE FRACTION
THE CORRECT ANSWER IS
3^5 = 243
9^5 = 59049
59049 / 243 = 243
IS MY ANSWER CORRECT ?!
THEY SUBTRACT THE EXPONENT AND THEN THEY SIMPLIFY THE FRACTION
THE CORRECT ANSWER IS
3^5 = 243
9^5 = 59049
59049 / 243 = 243
IS MY ANSWER CORRECT ?!
Answered by
drwls
3^5/9^5 = (3/9)^5
= (1/3)^5 = 1/3^5
= 1/243
Perhaps "the student" subtracted exponents because there was a division. You can only subtract exponents in division if you are dealing with powers of the same number.
= (1/3)^5 = 1/3^5
= 1/243
Perhaps "the student" subtracted exponents because there was a division. You can only subtract exponents in division if you are dealing with powers of the same number.
Answered by
PsyDAG
I searched Google under the key words "<I>math dividing powers</I>" to get this information:
Dividing Powers
What about dividing? Remember that dividing is just multiplying by 1-over-something. So all the laws of division are really just laws of multiplication. The extra definition of x-n as 1/xn comes into play here.
Example: What is x8€x6? Well, there are several ways to work it out. One way is to say that x8€x6 = x8(1/x6), but using the definition of negative exponents thatfs just x8(x-6). Now use the product rule (two powers of the same base) to rewrite it as x8+(-6), or x8-6, or x2. Another method is simply to go back to the definition: x8€x6 = (xxxxxxxx)€(xxxxxx) = (xx)(xxxxxx)€(xxxxxx) = (xx)(xxxxxx€xxxxxx) = (xx)(1) = x2. However you slice it, you come to the same answer: for division with like bases you subtract exponents, just as for multiplication of like bases you add exponents:
But therefs no need to memorize a special rule for division: you can always work it out from the other rules or by counting.
In the same way, dividing different bases canft be simplified unless the exponents are equal. x³€y² canft be combined because itfs just xxx/yy; But x³€y³ is xxx/yyy, which is (x/y)(x/y)(x/y), which is (x/y)³.
x^a/y^a = (x/y)^a
http://oakroadsystems.com/math/expolaws.htm#Multiply
I hope this helps. Thanks for asking.
Dividing Powers
What about dividing? Remember that dividing is just multiplying by 1-over-something. So all the laws of division are really just laws of multiplication. The extra definition of x-n as 1/xn comes into play here.
Example: What is x8€x6? Well, there are several ways to work it out. One way is to say that x8€x6 = x8(1/x6), but using the definition of negative exponents thatfs just x8(x-6). Now use the product rule (two powers of the same base) to rewrite it as x8+(-6), or x8-6, or x2. Another method is simply to go back to the definition: x8€x6 = (xxxxxxxx)€(xxxxxx) = (xx)(xxxxxx)€(xxxxxx) = (xx)(xxxxxx€xxxxxx) = (xx)(1) = x2. However you slice it, you come to the same answer: for division with like bases you subtract exponents, just as for multiplication of like bases you add exponents:
But therefs no need to memorize a special rule for division: you can always work it out from the other rules or by counting.
In the same way, dividing different bases canft be simplified unless the exponents are equal. x³€y² canft be combined because itfs just xxx/yy; But x³€y³ is xxx/yyy, which is (x/y)(x/y)(x/y), which is (x/y)³.
x^a/y^a = (x/y)^a
http://oakroadsystems.com/math/expolaws.htm#Multiply
I hope this helps. Thanks for asking.
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