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BECE Mathematics 2018 Paper

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Question : 26

Total: 40

Simplify

16^2 \times 8^2

$2^{10}$
$2^{14}$
$2^{15}$
$\; \; 2^{16}$

Solution:

Concept:

Express both numbers as powers of the same base, 2, and use the laws of indices.

Explanation:

Write

16

and

8

as powers of

2

:

16 = 2^4

and

8 = 2^3

.

So,

16^2 \times 8^2 = (2^4)^2 \times (2^3)^2

.

Using the power of a power rule,

(a^m)^n = a^{m \times n}

:

(2^4)^2 = 2^{4 \times 2} = 2^8

and

(2^3)^2 = 2^{3 \times 2} = 2^6

.

Now multiply the like bases using

a^m \times a^n = a^{m+n}

:

2^8 \times 2^6 = 2^{8+6} = 2^{14}

.

Therefore,

16^2 \times 8^2 = 2^{14}

.

Answer:

Option B:

2^{14}

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