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

Answers

Answer 1

Answer:

[tex]\boxed{a=4}[/tex]

Explanation:

Part 1. Finding product of [tex](4a^2)(4^3)[/tex]

Step 1. [tex]4^3=64[/tex]

Step 2. [tex](4a^2) * (64) = (64 * 4)(a^2)[/tex]

Step 3. [tex](64 * 4)(a^2) = 256a^2[/tex]

[tex]\boxed{(4a^{2})(4^3) = 256a^{2}}[/tex]

Part 2. Simplifying the equation & solving for a

Step 1. [tex]\sqrt{256a^{2}} = \sqrt{64^{2}}[/tex] ⇒ [tex]16a = 64[/tex]

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

[tex]\boxed{a = 4}[/tex]


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