Question

What is the value of (52 x 104)/(25 x 56)? (a) 0 (b) 2 (c) 5 (d) 10

Answer 1

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Answer 2

$\displaystyle \sf{ \frac{ {5}^{ - 2} \times {10}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } } = 2$

Given :

The expression

$\displaystyle \sf{ \frac{ {5}^{ - 2} \times {10}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } }$

To find :

The value of the expression is

(a) 0

(b) 2

(c) 5

(d) 10

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{ {5}^{ - 2} \times {10}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ \frac{ {5}^{ - 2} \times {10}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } }$

$\displaystyle \sf{ = \frac{ {5}^{ - 2} \times {(5 \times 2)}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } }$

$\displaystyle \sf{ = \frac{ {5}^{ - 2} \times {5 }^{ - 4} \times {2}^{ - 4} }{ {2}^{ - 5} \times {5}^{ - 6} } }$

$\displaystyle \sf{ = \frac{ {5}^{ - 2} \times {5 }^{ - 4} }{ {5}^{ - 6} } \times \frac{ {2}^{ - 4} }{ {2}^{ - 5} } }$

$\displaystyle \sf{ = \frac{ {5}^{ - 2 - 4} }{ {5}^{ - 6} } \times {(2)}^{ - 4 - ( - 5)} }$

$\displaystyle \sf{ = \frac{ {5}^{ - 6} }{ {5}^{ - 6} } \times {(2)}^{ - 4 + 5} }$

$\displaystyle \sf{ = {(5)}^{ - 6 + 6} \times {(2)}^{ 1} }$

$\displaystyle \sf{ = {(5)}^{ 0} \times {(2)}^{ 1} }$

$\displaystyle \sf{ = 1 \times 2 }$

$\displaystyle \sf{ = 2}$

Hence the correct option is (b) 2

Correct question : What is the value of (5⁻² x 10⁻⁴)/(2⁻⁵ x 5⁻⁶) (a) 0 (b) 2 (c) 5 (d) 10