Answers
9(x + y)
(7 - a)(b)
The Distributive Property is used in algebraic expressions to multiply a
single term and two or more terms which are inside a set of parentheses.
In the case of x(2y), there is only
one term inside the parenthesis
In the case of 9(x ∙ y), the distributive
property is not used because (x ∙ y) = xy which means only one term will be
multiplied by the term outside the parenthesis (9)
In the case of 9(x + y), the distributive
property is used because the two terms in the parenthesis (x and y) will be
multiplied by the term outside the parenthesis (9)
9(x + y) = 9*x + 9*y (by applying the distributive property)
In the case of (7 ∙ a)(b), the distributive
property is not used because (7 ∙ a) = 7a which means only one term will be
multiplied by the term outside the parenthesis (b)
In the case of (7 - a)(b), the distributive
property is used because the two terms in the parenthesis (7 and -a) will be
multiplied by the term outside the parenthesis (b)
(7 - a)(b) = 7*b - a*b (by applying the distributive
property)
In the case of (2 ∙ x) ∙ y, the distributive
property is not used because (2 ∙ x) = 2x which means only one term will be
multiplied by the term outside the parenthesis (y)
Assuming that an exponentiation sign is missing, all you need to know is that rational exponents work like this:
![a^{\frac{b}{c}}=\sqrt[c]{a^b}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Csqrt%5Bc%5D%7Ba%5Eb%7D)
So, you have
And similarly,
![81^{\frac{7}{4}}=\sqrt[4]{25^7}=\sqrt[4]{(3^4)^7}=3^7](https://tex.z-dn.net/?f=81%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D%3D%5Csqrt%5B4%5D%7B25%5E7%7D%3D%5Csqrt%5B4%5D%7B%283%5E4%29%5E7%7D%3D3%5E7)
