Please check these:
1.When the fraction 2/3 is used as exponent, wht role does the denominator 3 play in evaluating expression? I think it indicates cube root of the base,correct?
2.sqrt of (2^4x/4^-2x) is equilvalent to 2^4x, correct?
3.Simplify (2xy^-2z^4/y^-3/z^3)^2 would be 4x^2y^2z^2,correct?
4. (4x^2y^-4z)^3 simplified would be 64x^6z^3/y^12, correct
Thank you
1, correct
2. correct, good job on that one
3. not sure about the priority of the two divisions
I think the whole thing is squared, but you will need some additional brackets in that denominator
the way you typed it , it would be
[(2xy^-2 z^4) ( 1/y^-3) ( 1/z^3) ]^2 = 4x^2 y^2 z^2 which is your answer
OK then!
4. good again!
Thank you
what is the answer to this problem?
−x2+6zy=
x=10, y=−2, and z=−5.
1. When the fraction 2/3 is used as an exponent, the denominator 3 indicates the cube root of the base. In other words, it means taking the number to the power of 1/3. So, if the base is x, then x^(2/3) is equivalent to the cube root of x squared.
2. To simplify the expression, sqrt(2^4x/4^-2x), we can use the exponent rules. First, let's simplify the numerator: 2^4x = 2^(4x). Then, let's simplify the denominator: 4^-2x = (1/4^2x) = (1/16^x). Now, the expression becomes sqrt((2^(4x))/(1/16^x)).
To simplify the square root, we can bring the terms inside the square root together using the rule sqrt(a/b) = sqrt(a)/sqrt(b). Applying this rule, we have sqrt((2^(4x)) * (16^x)).
Now, we can simplify the expression further: sqrt(2^(4x) * 16^x) = sqrt((2^2x)^2 * (2^4x)). Using the rule sqrt(a^2 * b) = a * sqrt(b), we get (2^2x) * sqrt(2^4x).
Finally, simplifying the expression, we have (2^2x) * (2^2x) = 2^(2x + 2x) = 2^4x. Thus, the simplified expression is equivalent to 2^4x.
3. Let's simplify the expression (2xy^-2z^4/y^-3/z^3)^2 step by step:
First, we can simplify the numerator: 2xy^-2z^4 = 2x/z^2.
Next, we can simplify the denominator: y^-3/z^3 = z^3/y^3.
Now, we have (2x/z^2)^2 / (z^3/y^3), and using the rule (a/b)^n = (a^n)/(b^n), we can rewrite the expression as (2x)^2/(z^2)^2 * (y^3/z^3)^2.
Simplifying further, we have (4x^2)/(z^4) * (y^6)/(z^6).
Finally, combining the terms, we get 4x^2y^6/z^10, which is the simplified expression.
4. To simplify the expression (4x^2y^-4z)^3, we need to apply the exponent rule for raising a power to a power. When raising a power to a power, we multiply the exponents.
First, let's simplify the expression inside the parentheses: 4x^2y^-4z. Using the rule (a/b)^n = a^n/b^n, we can rewrite it as (4x^2/z^4) * (1/y^4) * z.
Now, let's raise this expression to the power of 3: (4x^2/z^4)^(3) * (1/y^4)^(3) * z^(3).
Applying the exponent rule, we get (4^3 * x^(2*3) * z^(4*3)) / (z^(4*3) * y^(4*3)) * z^3.
Simplifying further, we have 64x^6z^12 / (y^12 * z^12) * z^3.
Finally, combining the terms and canceling out z^12, we have 64x^6z^3 / y^12, which is the simplified expression.