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What is the value of c in the equation below?

2(to the negative fourth power) • 2 (to the positive second power) = a(To the power of “b”) = c

A) -4
B) -2
C) 1/64
D) 1/4

What is the value of c in the equation below 2to the negative fourth power 2 to the positive second power aTo the power of b c A 4 B 2 C 164 D 14 class=

Respuesta :

Answer:

D

Step-by-step explanation:

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] and [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

Given

[tex]2^{-4}[/tex] × 2² = [tex]2^{(-4+2)}[/tex] = [tex]2^{-2}[/tex] = c , hence

c = [tex]2^{-2}[/tex] = [tex]\frac{1}{2^{2} }[/tex] = [tex]\frac{1}{4}[/tex] → D

Stephen46

Answer:

The answer is option D.

Step-by-step explanation:

2^-4 • 2² = a^b = c

Use the rules of indices

Since the bases are the same and they are multiplying we add the exponents

That's

2^-4 + 2 = a^b = c

2^-2 = a^b = c

a^b = 2^-2

c = 1/4

Hope this helps you.

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