Question

If (4^a^-2)(4^3) = 64^2 , what is the value of a? a. 0 b. 4 c. 5 d. 7 e. 8

Answer 1

Answer:

$\boxed{a=4}$

Explanation:

Part 1. Finding product of $(4a^2)(4^3)$

Step 1. $4^3=64$

Step 2. $(4a^2) * (64) = (64 * 4)(a^2)$

Step 3. $(64 * 4)(a^2) = 256a^2$

$\boxed{(4a^{2})(4^3) = 256a^{2}}$

Part 2. Simplifying the equation & solving for a

Step 1. $\sqrt{256a^{2}} = \sqrt{64^{2}}$ ⇒ $16a = 64$

Step 2. $\frac{16a}{16} = \frac{64}{16}$   (divide both sides by coefficient of variable)

$\boxed{a = 4}$