Question

On Simplifying 8^3×2^4, we get. (a) 16^7 (b) 2^10 (c) 2 ^13 (d) 8^4​

Answer 1

Answer:

2^13

Step-by-step explanation:

8^3 can be written as 2^3^3 ie 2^9

so 2^9 + 2^4 = 2^13

Answer 2

$\bf \red{{8}^{3} \times {2}^{4} = {2}^{13} }$

Option (c) is correct.

Given:

• ${8}^{3} \times {2}^{4}$

To find:

• On simplification, what will be the result
• (a) 16^7
• (b) 2^10
• (c) 2^13
• (d) 8^4

Solution:

Concept / Formula to be used:

1. $\bf ( { {a}^{n} })^{m} = {a}^{nm}$
2. $\bf {a}^{n} \times {a}^{m} = {a}^{n + m}$

Step 1:

Rewrite the given expression.

As we know that

$8 = {2}^{3}$

so,

${8}^{3} \times {2}^{4} = ({ {2}^{3} )}^{3} \times {2}^{4}$

or

applying formula 1.

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

or

$= ({ {2} )}^{9} \times {2}^{4}$

Step 2:

Simplify using formula 2.

As base of both terms are equal and there is a multiplication sign in between.

So,

$= ({ {2} )}^{9 + 4}$

or

$= ({ {2} )}^{13}$

Thus,

$\bf {8}^{3} \times {2}^{4} = {2}^{13}$

Option (c) is correct.

Learn more:

1) Simplify: (3^-7×10^-8)÷(30)^-10

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2) simplify √1000X250

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