Select the equivalent expression.
start fraction, x, to the power 5 , divided by, x, to the power 5 , y, squared, y, to the power minus 3 , end fraction
x
5
y
2
y
−3
x
5
x
Fully simplify using only positive exponents.
start fraction, 14, x, to the power 8 , y, to the power 6 , divided by, 21, x, to the power 8 , y, squared, end fraction
21x
8
y
2
14x
8
y
6
27y^4 / 2
its wrong
I apologize for the mistake. Here is the correct simplification:
(14x^8 y^6) / (21x^8 y^2)
To simplify, we can divide the coefficients and subtract the exponents:
14 / 21 = 2/3
x^8 / x^8 = 1
y^6 / y^2 = y^(6-2) = y^4
Therefore, the fully simplified expression is:
(2/3)y^4
To find the equivalent expression, we can simplify the given expression by using the properties of exponents.
First, let's simplify the expression inside the numerator. We have x^5 divided by x^5, which results in 1 because any number divided by itself is equal to 1: x^5 / x^5 = 1.
Next, let's simplify the expression inside the denominator. We have y^2 times y^-3, which can be simplified using the property of exponents that states when you multiply two numbers with the same base, you add their exponents. Therefore, y^2 * y^-3 = y^(2 + (-3)) = y^(-1).
Now, we have 1 in the numerator and y^(-1) in the denominator. Any number or variable raised to the power of -1 is equivalent to its reciprocal. Therefore, y^(-1) can be written as 1/y.
So, the simplified expression is 1 / (1/y), which is equal to y.
Therefore, the equivalent expression is y.