Question

Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript one-fourth x?

Answer 1

Answer:

C 8 x/3

Step-by-step explanation:

Answer 2

Answer: Choice C

RootIndex 12 StartRoot 8 EndRoot Superscript x

12th root of 8^x = (12th root of 8)^x

$\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}$

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Explanation:

The general rule is

$\sqrt[n]{x} = x^{1/n}$

so any nth root is the same as having a fractional exponent 1/n.

Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)

$\sqrt[3]{8} = 8^{1/3}$

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Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so

(1/3)*(1/4)x = (1/12)x

In other words,

$\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/3)*(1/4)x}$

$\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/12)x}$

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From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this

$8^{(1/12)x} = \sqrt[12]{8^{x}}$

$8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x}$