Simplify each expression. Assume that no denominators are zero. Write each answer without using negative exponents.
The ^'s mean they're exponents
y^-3y^-4y^0
------------ <- division
(2y^-2)^3
numerator: y^-3y^-4y^0 = y^(-3-4)= y^-7
denominator: 2^3 * y^-6 = 8y^-6
numerator/denom= y^-7/8y^-6= 1/8 * y^(-7+6)
= 1/8 y^-1= 1/(8y)
I would multiply the denominator by itself three times, then move the terms with negative exponents up or down, changing the sign of the exponent, then combine terms. I hope this helps.
7/8y-6=8
To simplify the expression, let's start with the numerator: y^-3 * y^-4 * y^0.
To simplify this, we can use the property of exponents which states that when multiplying variables with the same base, you can add their exponents.
So, y^-3 * y^-4 * y^0 becomes y^(-3-4+0) = y^-7.
Now let's move on to the denominator: (2y^-2)^3.
To simplify this, we can use the property of exponents which states that when raising a power to another power, you multiply the exponents.
So, (2y^-2)^3 becomes 2^3 * (y^-2)^3 = 8 * y^(-2*3) = 8 * y^-6.
Now, we have the numerator y^-7 and the denominator 8 * y^-6.
To divide these expressions, we can use the property of exponents which states that when dividing terms with the same base, you subtract their exponents.
So, y^-7 divided by (8 * y^-6) becomes 1/8 * y^(-7-(-6)) = 1/8 * y^(-7+6) = 1/8 * y^-1.
Finally, to simplify the expression further, we can use another property of exponents which states that any number raised to the power of -1 is equal to its reciprocal.
So, y^-1 becomes 1/y.
Therefore, the simplified expression is 1/(8y).