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Mathematics

Evaluate :

(i) 74

(ii) (-5)3

(iii) (34)5\Big(\dfrac{3}{4}\Big)^5

(iv) (−52)2\Big(\dfrac{-5}{2}\Big)^2

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Answer

(i) 74

74 = 7 x 7 x 7 x 7 = 2401

Hence, the answer is 2401

(ii) (-5)

(-5)3 = (-5) x (-5) x (-5) = -125

Hence, the answer is -125

(iii) (34)5\Big(\dfrac{3}{4}\Big)^5

We know that (ab)n=anbn[Power of division rule]\Big(\dfrac{a}{b}\Big)^n = \dfrac{a^n}{b^n} \quad \text{[Power of division rule]}

∴(34)5=3545=3×3×3×3×34×4×4×4×4=2431024\therefore \Big(\dfrac{3}{4}\Big)^5 = \dfrac{3^5}{4^5} = \dfrac{3 \times 3 \times 3 \times 3 \times 3}{4 \times 4 \times 4 \times 4 \times 4} = \dfrac{243}{1024}

Hence, the answer is 2431024\dfrac{243}{1024}

(iv) (−52)2\Big(\dfrac{-5}{2}\Big)^2

(ab)n=anbn[Power of division rule]\Big(\dfrac{a}{b}\Big)^n = \dfrac{a^n}{b^n} \quad \text{[Power of division rule]}

(−52)2=(−5)222=(−5)×(−5)2×2=254=614\Big(\dfrac{-5}{2}\Big)^2 = \dfrac{(-5)^2}{2^2} = \dfrac{(-5) \times (-5)}{2 \times 2} = \dfrac{25}{4} = 6\dfrac{1}{4}

Hence, the answer is 6146\dfrac{1}{4}

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