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Surds and Indices Practice Test 1

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Question : 9 of 40

Marks: +1, -0

The value of

(8)^{-(2^{-2})}

is:

$2^{\frac{-1}{4}}$
$2^{\frac{-3}{4}}$
$2^{\frac{3}{4}}$
$2^{\frac{-1}{2}}$

Solution:

Concept:

Use exponent laws to simplify powers of powers and negative exponents.

Explanation:

Given expression:

(8)^{-(2^{-2})}

.

First simplify

2^{-2} = \dfrac{1}{2^2} = \dfrac{1}{4}

.

So the exponent becomes

-\dfrac{1}{4}

.

Now write

8

as

2^3

.

Thus,

(8)^{-1/4} = (2^3)^{-1/4}

.

Using

(a^m)^n = a^{mn}

, we get

2^{3 \times (-1/4)} = 2^{-3/4}

.

Answer:

2^{-3/4}

, which matches option B.

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