Question

Simplify and express the following as single exponent. 

(i) 2^-3 × 2^-2

(ii) 7^-2 × 7⁵

(iii) 3⁴ × 3^-5

(iv) 7⁵ × 7^-4 × 7^-6

(v) m⁵ × m^-10

(vi) (-5)^-3 × (-5)^-4

Answer 1

(i) 2^-3 × 2^-2 

= 2^(-3)+(-2) 

= 2^-5 = 1 / 2⁵ = 1 / 2×2×2×2×2    [∵ a^m × aⁿ = a^m+n]

= 1 / 32     

(ii) 7^-2 × 7⁵ 

= 7^-2+5 

= 7³ = 343

(iii) 3⁴ × 3^-5 

= 3^4+(-5)     [∵ a^-n = 1 / aⁿ]

= 3^-1 = 1 / 3

(iv) 7⁵ × 7^-4 × 7^-6 

= 7^5+(-4)+(-6) 

= 7^5-10 = 7^-5  =1/7⁵

(v) m⁵ × m^-10 

= m^5+(-10) = m^-5  = 1/m⁵

(vi) (-5)^-3 × (-5)^-4 

= (-5)^(-3)+(-4) 

= (-5)^-7 = 1/(−5)⁷ = –1 / 5⁷