Question

On simplifying 8 power 3 × 2 power 4 , we get

Answer 1

On simplifying 8³ × 2⁴ we get 2¹³

Correct question : On simplifying 8³ × 2⁴ we get (a) 16⁷ (b) 2¹³ (c) 2¹⁰ (d) 8⁴

Given :

The expression 8³ × 2⁴

To find :

On simplifying 8³ × 2⁴ we get

(a) 16⁷

(b) 2¹³

(c) 2¹⁰

(d) 8⁴

Formula Used :

We are aware of the formula on indices that :

$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

$\displaystyle \sf{2. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is 8³ × 2⁴

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf {8}^{3} \times {2}^{4}$

$\displaystyle \sf = {( {2}^{3}) }^{3} \times {2}^{4}$

$\displaystyle \sf = {2}^{(3 \times 3)} \times {2}^{4} \: \: \: \bigg[ \: \because \: { ({a}^{m} )}^{n} = {a}^{mn} \bigg]$

$\displaystyle \sf = {2}^{9} \times {2}^{4}$

$\displaystyle \sf = {2}^{(9 + 4)} \: \: \: \bigg[ \: \because \:{a}^{m} \times {a}^{n} = {a}^{m + n} \bigg]$

$\displaystyle \sf = {2}^{13}$

∴ On simplifying 8³ × 2⁴ we get 2¹³

Hence the correct option is (b) 2¹³

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