Simplify and write these in the exponential form. (i) 10⁻² × 10⁻⁵ (ii) 5⁷ ÷ 5⁴ (iii) 9⁻⁷ ÷ 9⁴ (iv) (13⁻²)⁻³ (v) m⁵n¹²(mn)⁹

(i) 10⁻⁷ (ii) 5³ (iii) 9⁻¹¹ (iv) 13⁶ (v) m¹⁴n²¹ — (i) Using n^a × n^b = n^(a+b): 10⁻² × 10⁻⁵ = 10⁻²⁺⁽⁻⁵⁾ = 10⁻⁷ (ii) Using n^a ÷ n^b = n^(a-b): 5⁷ ÷ 5⁴ = 5⁷⁻⁴ = 5³ (iii) Using n^a ÷ n^b = n^(a-b): 9⁻⁷ ÷ 9⁴ = 9⁻⁷⁻⁴ = 9⁻¹¹ (iv) Using (n^a)^b = n^(ab): (13⁻²)⁻³ = 13^(-2 × (-3)) = 13⁶ (v) First expand (mn)⁹ = m⁹n⁹. Then m⁵n¹² × m⁹n⁹ = m⁵⁺⁹n¹²⁺⁹ = m¹⁴n²¹

Simplify and write these in the exponential form. (i) 10⁻² × 10⁻⁵…

Question 5 of 28intermediate🔧 ApplyNumerical5 marks

Simplify and write these in the exponential form. (i) $10^{-2} \times 10^{-5}$ (ii) $5^7 \div 5^4$ (iii) $9^{-7} \div 9^4$ (iv) $(13^{-2})^{-3}$ (v) $m^5n^{12}(mn)^9$

(i)

Answer

$10^{-7}$

(ii)

Answer

$5^3$

(iii)

Answer

$9^{-11}$

(iv)

Answer

$13^6$

(v)

Answer

$m^{14}n^{21}$

Explanation

(i) Using $n^a \times n^b = n^{a+b}$ : $10^{-2} \times 10^{-5} = 10^{-2+(-5)} = 10^{-7}$ (ii) Using $n^a \div n^b = n^{a-b}$ : $5^7 \div 5^4 = 5^{7-4} = 5^3$ (iii) Using $n^a \div n^b = n^{a-b}$ : $9^{-7} \div 9^4 = 9^{-7-4} = 9^{-11}$ (iv) Using $(n^a)^b = n^{ab}$ : $(13^{-2})^{-3} = 13^{-2 \times (-3)} = 13^6$ (v) First expand $(mn)^9 = m^9n^9$ . Then $m^5n^{12} \times m^9n^9 = m^{5+9}n^{12+9} = m^{14}n^{21}$

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