Rules of Indices

Product Laws

$(1)\,\,\,\,$ $b^{\displaystyle m} \times b^{\displaystyle n} = b^{\displaystyle m+n}$

Learn the proof of product rule of exponential terms having same base and its verification.

$(2)\,\,\,\,$ $b^{\displaystyle m} \times c^{\displaystyle m} = {(b \times c)}^{\displaystyle m}$

Learn the proof of product law of exponential terms having same exponent and know how to verify it.

Division Rules

$(1)\,\,\,\,$ $\dfrac{b^{\displaystyle m}}{b^{\displaystyle n}} = b^{\displaystyle m-n}$

Learn how to derive the division rule of exponential terms having same base and its mathematical verification.

$(2)\,\,\,\,$ $\dfrac{b^{\displaystyle m}}{c^{\displaystyle m}} = {\Bigg(\dfrac{b}{c}\Bigg)}^{\displaystyle m}$

Observe the proof of division rule of exponential terms having same exponent and know the verification.

Power formulas

$(1)\,\,\,\,$ ${(b^{\displaystyle m})}^{\displaystyle n} = b^{\displaystyle mn}$

Learn power rule of exponential term having another exponent and understand the verification of this identity in number system.

$(2)\,\,\,\,$ $b^{\displaystyle -m} = \dfrac{1}{b^{\displaystyle m}}$

$(3)\,\,\,\,$ $b^{\frac{m}{n}} = \sqrt[\displaystyle n]{b^{\displaystyle m}}$

$(4)\,\,\,\,$ $b^0 = 1$

$(5)\,\,\,\,$ $b^1 = b$

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