Now, there's a property of exponents that on having same bases, the powers can be compared as well as when these identical bases are multiplied to each other, their powers are added.
[Note - In the above question, if instead of multiplication the identical bases were divided then their powers would have been subtracted rather than being added]
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Required Answer -
Explanation -
Now, there's a property of exponents that on having same bases, the powers can be compared as well as when these identical bases are multiplied to each other, their powers are added.
[tex] \sf \to \: {a}^{m} = {a}^{n} \implies \: m = n[/tex]
[tex] \sf \to \: {a}^{m} \times {a}^{n} = {a}^{a} \implies \: m + n = a[/tex]
On comparing -
⟹ (m + 1) + 5 = 7
⟹ m + 6 = 7
⟹ m = 7 - 6 = 1
⟹ m = 1
★ Verification -
[tex] \sf \to \: {3}^{m + 1} \times {3}^{5} = {3}^{7} [/tex]
Put the value of m = 1 (calculated)
[tex] \sf \to \: {3}^{1 + 1} \times {3}^{5} = {3}^{7} [/tex]
[tex]\sf \to \: {3}^{2} \times {3}^{5} = {3}^{7} [/tex]
[tex] \to \: \bf {3}^{7} = {3}^{7} [/tex]
L.H.S = R.H.S
Hence Verified!
[Note - In the above question, if instead of multiplication the identical bases were divided then their powers would have been subtracted rather than being added]