A STUDENT SAID THAT 3^5 / 9^5 IS THE SAME AS 1/3 . WHAT MISTAKE HAS THE STUDENT MADE ?
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.
I searched Google under the key words "math dividing powers" 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 that�fs 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 there�fs 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 can�ft be simplified unless the exponents are equal. x³�€y² can�ft be combined because it�fs 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.
To identify the mistake made by the student, let's simplify the equation and compare both sides.
The student claimed that 3^5 / 9^5 is the same as 1/3.
To simplify this, let's start by evaluating the exponents individually:
3^5 = 3 * 3 * 3 * 3 * 3 = 243
9^5 = 9 * 9 * 9 * 9 * 9 = 59,049
Now, let's substitute these values back into the equation:
243 / 59,049 = 1/3
Simplifying the fraction 243 / 59,049 is not equal to 1/3. The correct decimal value is approximately 0.004122.
Therefore, the mistake the student made is claiming that 3^5 / 9^5 is the same as 1/3, which is incorrect.
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 ?!