Test Index

Indices

© examsnet.com

Question : 8 of 86

Marks: +1, -0

The value of is

\;\frac{(243)^{0.13} \times (243)^{0.07}}{(7)^{0.25} \times (49)^{0.075} \times (343)^{0.2}}

$\;\frac{3}{7}$
$\;\frac{7}{3}$
$1\;\frac{3}{7}$
$2\;\frac{2}{7}$

Solution:

Concept:

Simplify powers using prime factorization and exponent laws.

Explanation:

Write each base as a power of a prime:

243 = 3^5

,

49 = 7^2

,

343 = 7^3

.

Numerator:

(3^5)^{0.13} \times (3^5)^{0.07} = 3^{5 \times 0.13} \times 3^{5 \times 0.07} = 3^{0.65} \times 3^{0.35} = 3^{0.65+0.35} = 3^1 = 3

.

Denominator:

7^{0.25} \times (7^2)^{0.075} \times (7^3)^{0.2} = 7^{0.25} \times 7^{2 \times 0.075} \times 7^{3 \times 0.2} = 7^{0.25} \times 7^{0.15} \times 7^{0.6} = 7^{0.25+0.15+0.6} = 7^1 = 7

.

Thus, the value is

\frac{3}{7}

.

Answer:

\frac{3}{7}

© examsnet.com

Go to Question:

Prev Question

Next Question