Exponents Of Real Numbers — Maths STD 9 — Question
Maharashtra BoardEnglish MediumSTD 9MathsExponents Of Real Numbers2 Marks
Question
State the power law of exponents.
✓
Answer
The "power rule" tell us that to raise a power to a power, just multiply the exponents.
If $a$ is any real number and $m, n$ are positive integers, then $\left(a^m\right)^n=a^{m n}$
We have,
$\left(a^m\right)^n=a^m \times a^m \times a^m \times \ldots n \text { factors } \\
\left(a^m\right)^n=(a \times a \times a \times \ldots m) \times(a \times a \times a \times \ldots m) \ldots n \text { factors } \\
\left(a^m\right)^n=(a \times a \times a \times \ldots m n)$
Hence, $\left(a^m\right)^n=a^{m n}$
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