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Question : 2 of 86

Marks: +1, -0

[(18)^{3.5} \div (27)^{3.5}] \times 6^{3.5}=2^{x}

then the value of

x

is

3.5
4.5
6
7

Solution:

Concept:

Simplify the powers using the property

(a^m \div b^m) \times c^m = \left(\frac{a}{b} \times c\right)^m

.

Explanation:

Given:

[(18)^{3.5} \div (27)^{3.5}] \times 6^{3.5} = 2^x

.

Combine exponents:

\left(\frac{18}{27}\right)^{3.5} \times 6^{3.5} = \left(\frac{18}{27} \times 6\right)^{3.5}

.

Simplify

\frac{18}{27} = \frac{2}{3}

, so

\frac{2}{3} \times 6 = 4

. Thus left side equals

4^{3.5}

.

Write

4 = 2^2

:

(2^2)^{3.5} = 2^{2 \times 3.5} = 2^7

. Hence

x = 7

.

Answer:

x = 7

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