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Question : 5 of 86

Marks: +1, -0

If

(25)^{7.5} \times (5)^{2.5} \div (125)^{1.5} = 5^{x},

x=

8.5
13
16
None

Solution:

Concept:

Express all numbers as powers of the same base to combine exponents.

Explanation:

Convert

25

,

5

, and

125

to powers of

5

:

25 = 5^2

,

125 = 5^3

.

Then

(25)^{7.5} = (5^2)^{7.5} = 5^{2 \times 7.5} = 5^{15}

.

(5)^{2.5} = 5^{2.5}

.

(125)^{1.5} = (5^3)^{1.5} = 5^{3 \times 1.5} = 5^{4.5}

.

The expression becomes

5^{15} \times 5^{2.5} \div 5^{4.5}

.

Using laws of exponents:

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

and

a^m \div a^n = a^{m-n}

:

5^{15 + 2.5 - 4.5} = 5^{13}

.

Thus

5^x = 5^{13}

, so

x = 13

.

Answer:

x = 13

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