write with postive exponents. Assume that even roots are nonnegative quantities and the demoninators are non zero
(2x/y^2)-^4
To write the expression with positive exponents, we need to take the reciprocal and get rid of the negative exponent.
First, let's rewrite the expression with a positive exponent:
(2x/y^2)^(-4)
Now, let's apply the rule for negative exponents. The rule states that any term with a negative exponent can be written as the reciprocal with a positive exponent:
(2x/y^2)^(-4) = 1 / (2x/y^2)^4
Next, we can simplify the expression inside the parentheses by raising each term to the power of 4:
1 / (2x/y^2)^4 = 1 / (2^4 * x^4 / y^8)
Now, let's simplify further by multiplying the numerator by the reciprocal of the denominator:
1 / (2^4 * x^4 / y^8) = y^8 / (2^4 * x^4)
Finally, we can simplify the expression by evaluating 2^4, which is 16:
y^8 / (2^4 * x^4) = y^8 / (16 * x^4)
So, the expression (2x/y^2)^(-4) can be rewritten as y^8 / (16 * x^4) with positive exponents.