Question

${7}^{2 {n}^{ + 1} } \div 49 = {7}^{3}$
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Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

=>7²ⁿ⁺¹ ÷ 49 = 7³

Concepts

• If bases are same then power gets added during multiplication and gets substracted during division.

E.g., => aᵐ× aⁿ = aᵐ⁺ⁿ

In division=> aᵐ ÷ aⁿ = aᵐ⁻ⁿ

=>7²ⁿ⁺¹ ÷ 49 = 7³

We can also write 49 as 7×7 or 7²

=>7²ⁿ⁺¹ ÷ 7²= 7³

Note: here bases are same which is 7 but their power is different and are in division form so,their powers gets substracted according to our concepts.

=>7²ⁿ⁺¹⁻² = 7³

=>7²ⁿ⁻¹= 7³

Now, equating both sides :

Note : here bases are same on both sides so,both bases gets automatically cancelled.

=>2n-1=3

=>2n= 3+1

=>2n= 4

=>n= 4÷ 2=2

n=2

Check

=>7²ⁿ⁺¹ ÷ 49 = 7³

=>7²⁽²⁾⁺¹ ÷ 7²

=> 7⁵÷ 7²

=>7⁵⁻²

=>7³

LHS=RHS (verified)