if the expression(2ya)4 is equivalent to 16y8 what is the value of a
To find the value of "a," we can set up an equation based on the information given. Let's start by writing out the expression (2ya)^4 in expanded form:
(2ya)^4 = 16y^8
Now, let's simplify each side of the equation step by step:
On the left side, raising a power to another power means we multiply the exponents. So, we can rewrite (2ya)^4 as (2^4)(y^4)(a^4).
(2^4)(y^4)(a^4) = 16y^8
Since 2^4 equals 16, we can substitute it into the equation:
16(y^4)(a^4) = 16y^8
Now, we can cancel out the 16 on both sides:
(y^4)(a^4) = y^8
To equate the exponents, we can write:
a^4 = y^(8-4)
Simplifying further:
a^4 = y^4
To solve for "a," we need to take the fourth root of both sides:
∛ a^4 = ∛ y^4
This gives us:
a = y
So, the value of "a" is equal to "y" based on the given expression and equation.