Write the following expressions as a power of a power in at least…

Question 14 of 28intermediate🔧 ApplyShort Answer4 marks

Write the following expressions as a power of a power in at least two different ways: (i) $8^6$ (ii) $7^{15}$ (iii) $9^{14}$ (iv) $5^8$

(i)

Answer

$8^6 = (8^2)^3 = (8^3)^2$

(ii)

Answer

$7^{15} = (7^3)^5 = (7^5)^3$

(iii)

Answer

$9^{14} = (9^2)^7 = (9^7)^2$

(iv)

Answer

$5^8 = (5^2)^4 = (5^4)^2$

Explanation

(i) Since $6 = 2 \times 3 = 3 \times 2$ , we have $8^6 = (8^2)^3 = (8^3)^2$ (ii) Since $15 = 3 \times 5 = 5 \times 3$ , we have $7^{15} = (7^3)^5 = (7^5)^3$ (iii) Since $14 = 2 \times 7 = 7 \times 2$ , we have $9^{14} = (9^2)^7 = (9^7)^2$ (iv) Since $8 = 2 \times 4 = 4 \times 2$ , we have $5^8 = (5^2)^4 = (5^4)^2$

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