Represent the following expressions as a power of the number a (a≠0):
(a^2a^4)÷a^−3/a÷(a^2a^3)^4
(a^2a^4)÷a^−3 = (a^2a^4)*a^3 = a^6*a^3 = a^9
a/(a^2a^3)^4 = a/(a^5)^4 = a/a^20 = a^-19
a^9÷a^-19 = a^9 * a^19 = a^28
To express the given expressions as a power of the number "a", we can make use of the laws of exponents. Let's break down the expressions step by step:
Expression 1: (a^2a^4)÷a^−3
To simplify this expression, we can apply the multiplication and division properties of exponents. When dividing with the same base, we subtract the exponents.
(a^2a^4)÷a^−3 = a^(2+4-(-3))
Simplifying the exponent with the negative sign:
= a^(2+4+3)
= a^9
So, the first expression (a^2a^4)÷a^−3 can be represented as a^9.
Expression 2: a÷(a^2a^3)^4
Here, we need to simplify the expression within the parentheses (a^2a^3) first.
(a^2a^3) = a^(2+3)
= a^5
Now, let's combine this result with the outer expression.
a÷(a^2a^3)^4 = a÷(a^5)^4
= a÷a^(5*4)
= a÷a^20
= a^(1-20)
= a^(-19)
Therefore, the second expression a÷(a^2a^3)^4 can be represented as a^(-19).
To summarize:
Expression 1: (a^2a^4)÷a^−3 can be represented as a^9.
Expression 2: a÷(a^2a^3)^4 can be represented as a^(-19).