Question

Fill in the Blank am = an = a........
Where m and n are natural numbers:​

Answer 1

Answer:

a^m + a^n = a^m+n

Answer 2

Correct question: $a^m$ ÷ $a^n$ = ......, where m, n are natural numbers.

Answer:

The value of $a^m$ ÷ $a^n$ is $a^{m-n}$.

Step-by-step explanation:

Let suppose $y$ = $a^m$ ÷ $a^n$, where $m,n$ are natural numbers.

⇒ $y=\frac{a^m}{a^n}$ ...... (1)

Take logarithm both the sides as follows:

⇒ $logy=log\left(\frac{a^m}{a^n} \right)$

⇒ $logy=log(a^m )-log(a^n)$ (Since log$\left(\frac{a}{b} \right)$ = log a - log b)

⇒ $logy=m loga-nloga$ (Since log $a^b$ = b log a)

Take log(a) common as follows:

⇒ $logy=$$(m-n)$ $loga$

Using the property, b log a =  log $a^b$,

⇒ $logy=$ $log(a^{m-n})$

Take exponential (or anti-log) both sides.

⇒ $e^{logy}=$ $e^{log(a^{m-n})}$

⇒ $y=$ $a^{m-n}$ (Since $e^{loga}=a$) ...... (2)

From (1) and (2),

⇒ $\frac{a^m}{a^n}=a^{m-n}$, where $m,n$ are natural number.

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