(2^-3)(x^0(x^2))
all over _______
(x^-3)(xy^-3)(y)
does it equal
x^2)(xy^3)(x^3)
______________
8y
Well, the way you typed it I get
x^2 x^3 y^3
-------------
8 x y
or
x^4 y^2
--------------
8
My high school offered Algebra III as well.
To simplify the given expression, let's break it down step by step:
First, let's simplify the numerator:
(2^-3)(x^0)(x^2)
The exponent of 0 means any number raised to the power of 0 equals 1. So we can simplify this to:
(2^-3)(1)(x^2)
Next, let's simplify the denominator:
(x^-3)(xy^-3)(y)
Using the rule of exponents, when you have negative exponents, you can move the terms to the opposite side of the fraction and change the sign of the exponent:
1/(x^3)(x)(y^3)(y)
Now, let's simplify the entire expression:
[(2^-3)(1)(x^2)] / [1/(x^3)(x)(y^3)(y)]
Multiplying the entire expression by the reciprocal of the denominator:
[(2^-3)(1)(x^2)] * [(x^3)(x)(y^3)(y)/1]
Now, combining like terms and simplifying:
(2^-3)(1)(x^2)(x^3)(x)(y^3)(y)
Using the rule of exponents, multiplying the terms with the same base, you add their exponents:
2^-3 means 1 / (2^3) = 1 / 8
Combining all the terms together, we get:
[(1/8)(x^2)(x^3)(x)(y^3)(y)] / 1
Multiplying all the variables together:
(1/8)(x^2)(x^3)(x)(y^3)(y) = x^(2+3+1) * y^(3+1+1) = x^6 * y^5
Finally, substituting the obtained value in the expression:
(x^6 * y^5) / 8y
Therefore, the simplified expression is:
(x^6 * y^5) / 8y