LUANDATO wrote:Simplify,
$$(4^y+4^y+4^y+4^y)\cdot(3^y+3^y+3^y)$$
$$\left(A\right)\ 4^{4y}\cdot3^{3y}$$
$$(B)12^{y+1}$$
$$(C)16^y+9^y$$
$$(D)12^y$$
$$(E)4^y*12^y$$
Let y=-1.
Plugging y=-1 into the given expression, we get:
(4¯¹ + 4¯¹ + 4¯¹ + 4¯¹)(3¯¹ + 3¯¹ + 3¯¹) = (1/4 + 1/4 + 1/4 + 1/4)(1/3 + 1/3 + 1/3) = (1)(1) = 1.
The target value is 1.
Now plug y=-1 into the answers to see which yields the target value of 1.
A: 4¯� + 3¯³ = 1/(4�) + 1/(3³) ≠1.
B: 12� = 1.
C: 16¯¹ + 9¯¹ = (1/16) + (1/9) ≠1.
D: 12¯¹ = 1/12 ≠1.
E: 4¯¹ * 12¯¹ = (1/4)(1/12) ≠1.
Only
B works.
The correct answer is
B.
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