Question

choose the correct alternative : 100¹⁰⁰ is equal to (a) 2¹⁰⁰ × 50¹⁰⁰ (b) 2¹⁰⁰ + 50¹⁰⁰ (c) 2² × 50⁵⁰ (d) 2² + 50⁵⁰​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

100¹⁰⁰ is equal to

(a) 2¹⁰⁰ × 50¹⁰⁰

(b) 2¹⁰⁰ + 50¹⁰⁰

(c) 2² × 50⁵⁰

(d) 2² + 50⁵⁰

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf {(ab)}^{n} = {a}^{n} \times {b}^{n}$

EVALUATION

Here the given expression is

$\sf {100}^{100}$

We now use the formula

$\boxed{ \: \: \sf {(ab)}^{n} = {a}^{n} \times {b}^{n} \: \: }$

$\sf {100}^{100}$

$\sf = {(2 \times 50)}^{100}$

$\sf = {2 }^{100} \times {50}^{100}$

FINAL ANSWER

Hence the correct option is (a) 2¹⁰⁰ × 50¹⁰⁰

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Answer 2

Answer:

CHOOSE THE CORRECT OPTION

100¹⁰⁰ is equal to

(a) 2¹⁰⁰ × 50¹⁰⁰

(b) 2¹⁰⁰ + 50¹⁰⁰

(c) 2² × 50⁵⁰

(d) 2² + 50⁵⁰

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

\sf {(ab)}^{n} = {a}^{n} \times {b}^{n}(ab)

n

=a

n

×b

n

EVALUATION

Here the given expression is

\sf {100}^{100}100

100

We now use the formula

\boxed{ \: \: \sf {(ab)}^{n} = {a}^{n} \times {b}^{n} \: \: }

(ab)

n

=a

n

×b

n

\sf {100}^{100}100

100

\sf = {(2 \times 50)}^{100}=(2×50)

100

\sf = {2 }^{100} \times {50}^{100}=2

100

×50

100

FINAL ANSWER

Hence the correct option is (a) 2¹⁰⁰ × 50¹⁰⁰