WAEC MATHEMATICS QUESTIONS ON INDICES  

Introduction to solving Waec questions on indices

What are indices(Waec questions on indices)

How to solve Waec questions on indices(Waec 2023)

Laws of indices. 

1. Laws of indices #1: $a^0 = 1$. For this law,  any number or letter raised to the power of 0 is equivalent to one. 
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   Mathematically,  $2^0 = 1, b^0 = 1, (2.6)^0 = 1, (anything)^0 = 1$.
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2. Laws of indices #2: $a^1 = a$. Here, anything raised to the power of one remains unchanged.
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   Meaning,  $10^1 = 10, 9^1 = 9$
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3. Laws of indices #3: $a^m × a^n = a^{m+n}$, it should be noted that all laws of indices only work for the same base. 
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   Example; $2^3 × 2^4$;
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   According to the third law, the above question $2^3 × 2^4$ can be simplified to give the expression below;
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   $2^3 × 2^4 = 2^{3+4}$
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   $2^3 × 2^4 = 2^{7}$
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4. Law of indices #4: $\dfrac{a^m} {a^n}$ or $a^m ÷ a^n = a^{m-n}$
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   Example: $\dfrac{2^6}{2^4}$
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   According to indices law 4, the above expression can be reduced to $2^{6-4}$;
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   Simplifying the numerator gives;
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   $2^2$
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5. Law of indices #5: $(a^m) ^n = a^{m×n}$
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   Example: $(3^2)^5$
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   According to law 5, the above expression can be simplified to;
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   $3^{2×5}$
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   Simplifying further;
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   $3^{10}$ that's the final answer
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6. Laws of indices #6: $a^{-m} = \dfrac{1}{a^m}$
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   Example: $2^{-3}$
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   $2^{-3} = \dfrac{1}{2^3}$
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   Simplifying the denominator further gives;
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   $\dfrac{1}{8}$. Final answer
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7. Law of indices #7: $a^{\frac{1} {n}} = \sqrt[n] {a}$ :
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   Where $\sqrt[n] {a}$ : Means nth root of base a
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   Example; $27^{\frac{1} {3}}$ :
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   Following law 7
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   $27^{\frac{1} {3}} = \sqrt[3] {27}$ :
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   $\sqrt[3] {27}$  means the third root of 27. The third root of 27 is 3 since 3×3×3 gives 27.
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   Therefore;
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   $\sqrt[3] {27} = 3$
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   Final answer = 3
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8. Law of indices #8: $a^{\frac{m} {n}} = (\sqrt[n] {a})^m$
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   Example: $8^{\frac{2} {3}}$
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   Following law 8:
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   $8^{\frac{2} {3}} = (\sqrt[3] {8})^2$
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   First, let's reduce the term to bracket. The term in the bracket means the cube root of 8. Since the cube root of 8 is 2.
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   Therefore ;
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   $8^{\frac{2} {3}} = (2)^2$
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   Finally;
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   $8^{\frac{2} {3}} = 4$
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   Final answer = 4
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9. Laws of indices #9: $\left(\dfrac{a} {b}\right) ^m = \dfrac{a^m} {b^m}$
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   Example: $\left(\dfrac{2} {3}\right) ^3$
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   Following law 9:
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   $\left(\dfrac{2} {3}\right) ^3 = \dfrac{2^3} {3^3}$
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   Simplifying further;
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   $\left(\dfrac{2} {3}\right) ^3 = \dfrac{8} {27}$. 
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   Mathematically: $\sqrt{a} = \sqrt{b×c}$ where b must be a perfect square and c can be any integer
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Solved Waec past questions on indices(How to solve indices)

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