(100x^3y^-2)/(64x^7y^4)
Please simplify completely :)
100/64 = 25/16
x^3 / x^7 = 1/x^4
y^-2 / y^4 = 1/y^6
so (100x^3y^-2)/(64x^7y^4)
=25/(16 x^4 y^6)
wait isn't (y^-2)/(y^4)=y^2?
nope
(y^-2) times y^4 would be y^2, but you were dividing, so you have to subtract the exponents
-2 - 4 = -6
Ohh right thank you
To simplify the expression (100x^3y^-2)/(64x^7y^4), you can follow these steps:
Step 1: Rewrite the expression using positive exponents:
(100x^3 / 64x^7) * (1 / y^2y^4)
Step 2: Simplify the coefficient:
100 / 64 can be simplified by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor is 4.
Dividing 100 by 4 gives 25, and dividing 64 by 4 gives 16.
So, the coefficient simplifies to 25 / 16.
Step 3: Simplify the x terms:
Since both terms have x as the base, you can subtract the exponents:
x^3 / x^7 = x^(3-7) = x^(-4).
Remember, when subtracting exponents with the same base, you subtract the exponents and keep the base.
Step 4: Simplify the y terms:
Since both terms have y as the base, you can subtract the exponents:
1 / y^2y^4 = 1 / y^(2+4) = 1 / y^6
Similarly, when adding exponents with the same base, you add the exponents and keep the base.
Combining the simplified terms, the expression becomes:
(25/16) * (x^(-4)) * (1 / y^6)
Now, to simplify further, you can apply the following rules:
- Negative exponents can be rewritten as positive exponents by moving the base to the opposite side of the fraction:
x^(-4) = 1 / x^4
- Multiplying terms with the same base (x) means adding their exponents:
(x^(-4)) = 1 / x^4
So, the final simplified expression is:
(25/16) * (1 / x^4) * (1 / y^6)
Alternatively, if you prefer the expression without any negative exponents, you can move the terms with negative exponents to the denominator and make them positive:
(25/16) / (x^4 * y^6)
This represents the same value as the previous expression but without negative exponents.