Test Index

Indices

© examsnet.com

Question : 4 of 86

Marks: +1, -0

The value of

\; \frac{1}{(216)^{-\; \frac{2}{3}}} + \; \frac{1}{(256)^{-\; \frac{3}{4}}} + \; \frac{1}{(32)^{-\; \frac{1}{5}}}

is

102
105
107
109

Solution:

Concept:

Use

a^{-n} = \frac{1}{a^n}

to rewrite each term as a positive power, then simplify using exponent rules.

Explanation:

Step 1:

\frac{1}{(216)^{-2/3}} = 216^{2/3}

.

Step 2:

216 = 6^3

, so

216^{2/3} = (6^3)^{2/3} = 6^{2} = 36

.

Step 3:

\frac{1}{(256)^{-3/4}} = 256^{3/4}

.

Step 4:

256 = 4^4

, so

256^{3/4} = (4^4)^{3/4} = 4^{3} = 64

.

Step 5:

\frac{1}{(32)^{-1/5}} = 32^{1/5}

.

Step 6:

32 = 2^5

, so

32^{1/5} = (2^5)^{1/5} = 2

.

Step 7: Sum =

36 + 64 + 2 = 102

.

Answer:

102

© examsnet.com

Go to Question:

Prev Question

Next Question