If $1960 = 2^{a .} 5^{b .} 7^{c},$ find $a, b a n d c .$ . Calculate the value of $2^{- a} \times 7^{b} \times 5^{- c}$

Open in App

Solution

Step-1: Finding the value of a, b and c
$1960 = 2^{a .} 5^{b .} 7^{c},$
∴Prime factorization of
$1960 = 2 \times 2 \times 2 \times 5 \times 7 \times 7$
$= 2^{3} \times 5^{1} \times 7^{2}$
$∵ 2^{3} \times 5^{1} \times 7^{2} = 2^{a} {.5}^{b} {.7}^{c}$
By comparing the same bases and their indices, we get:
$a = 3, b = 1 a n d c = 2$
Step-2: Calculating the value of
$2^{- a} \times 7^{b} \times 5^{- c}$
Now,
$= 2^{- a} \times 7^{b} \times 5^{- c}$
$= 2^{- 3} \times 7^{1} \times 5^{- 2}$
$= 7 \times \frac{1}{2^{3}} \times \frac{1}{5^{2}}$
$[∵ a^{- 1} = \frac{1}{a}]$
$= 7 \times \frac{1}{8 \times 25}$
$= \frac{7}{200}$
Hence, the value of $2^{- a} \times 7^{b} \times 5^{- c} = \frac{7}{200}$

Suggest Corrections

Similar questions

If $2160 = 2^{a} . 3^{b} . 5^{c}$ , find a, b and c. Hence calculate the value of $3^{a} \times 2^{- b} \times 5^{- c}$

\vec{a} and \vec{b}

|\vec{a}| = 2, |\vec{b}| = 1 and \vec{a} \cdot \vec{b} = 1,

(3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) .

If 1176 = $2^{a} \times 3^{b} \times 7^{c}$ , find a, b and c.

1960 =

2^{a} \cdot 5^{b} \cdot 7^{c}

2^{- a} \cdot 7^{b} \cdot 5^{- c}

1960 = 2^{a} . 5^{b} . 7^{c}

a

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program