Question

The value of
$\frac{ {128}^{ \frac{1}{7} } \times {343}^{ \frac{1}{3} } }{( {4}^{4}) {}^{ \frac{3}{4} } }$
A )
$\frac{5}{32}$
B)
$\frac{7}{32}$
C)
$\frac{11}{32}$
D)
$\frac{15}{32}$
​

Answer 1

Answer:

C) 7/32

Step-by-step explanation:

First we will solve numerator, then denominator, then we will divide

Numerator:

= $128^{\frac{1}{7}}$ x $343^{\frac{1}{3}}$

= $(2^7)^{\frac{1}{7}}$ x $(7^3)^{\frac{1}{3}}$  (as $128 = 2^7$ and $343 = 7^3$)

$(a^m)^n = a^{mn}$  [It is law of exponents]

= $2^1$ x $7^1$     (as 1/7 x 7 = 1 and 1/3 x 3 = 1)

= 2 x 7  ($a^1 = a [Law of exponents]$

= 14

Denominator:

$= (4^4)^{\frac{3}{4}}\\\\(a^m)^n = a^{mn}\\= 4^3$(as 4 x 3/4 = 3)

= 4 x 4 x 4 = 64

Fraction:

$= \frac{14}{64} \\= \frac{7}{32}$