What would the ⍰ need to be in the expression below for the simplified form of the expression to be equal to
1/(8xy^6 )?
(4x^2 y^(-5))/(2^⍰ x^3 y)
The ⍰ would need to be equal to 10.
To simplify the expression (4x^2 y^(-5))/(2^⍰ x^3 y), we need to apply the rules of exponents.
First, we can simplify the numerator by multiplying the x^2 and x^3 terms together, resulting in x^(2+3) = x^(5).
Next, we can simplify the y^(-5) term by applying the rule that states y^(-n) = 1/y^n. So, y^(-5) = 1/y^5.
Now our expression becomes:
(4x^5)/(2^⍰ y^5)
To make the denominator equal to 8xy^6, we need to get rid of the 2^⍰ term and replace it with 8.
Since 2^3 = 8, we can rewrite the expression as:
(4x^5)/(2^⍰ y^5) = (4x^5)/(2^3 y^5) = (4x^5)/(8y^5) = (x^5)/(2y^5)
Finally, to make the expression equal to 1/(8xy^6), we need to remove the x^5 term in the numerator.
To cancel out the x^5 term, we can divide both the numerator and denominator by x^5.
Therefore, the ⍰ would need to be equal to 10 to make the simplified form of the expression equal to 1/(8xy^6).