Question

Find the appropriate number in place of the symbol ’?’ in the following. 
Let ‘k’ be any non-zero integer.

i) k³ × k⁴ = k^?

ii) k¹⁵ × k^? = k³¹

Answer 1

i) k³ × k⁴ = k^?

as k³ × k⁴ = k³⁺⁴ = k⁷ the value of ‘?’ = 7

ii) k¹⁵ × k^? = k³¹

as k¹⁵ × k^? = k^15+?

but k^{15 + ?} = k³¹

Since bases are equal we equate the exponents

∴ 15 + ? = 31

(i.e„) ? = 31 – 15 = 16