Simplify using laws of exponents.(i) 35 x 38(ii) a4 x a10(iii) 7x x

1.	Simplify using laws of exponents.(i) 35 x 38(ii) a4 x a10(iii) 7x x 72(iv) 25 ÷ 23(v) 188 ÷ 184(vi) (64)3(vii) (xm)0(viii) 95 x 35(ix) 3y x 12y(x) 256 x 56
Answer» (i) 3⁵ x 3⁸ [since a^m x aⁿ = a^{m + n}] = 3^{5 + 8} = 3¹³ (ii) a⁴ x a¹⁰ = a^{4 + 10} = a¹⁴ (iii) 7^x x 7²= 7^{x + 2} (iv) 2⁵ ÷ 2³ [since \(\frac{a^m}{a^n}\) = a^{m - n}] = 2^{5 - 3} = 2² (v) 18⁸ ÷ 18⁴ = 18^{8 - 4} = 18⁴ (vi) (6⁴)³ [since (a^m)ⁿ = a^{m x n}] = 6^{4 x 3} = 6¹² (vii) (x^m)⁰ [since (a^m)ⁿ = a^{m x n}; a⁰ = 1] = x^{m x 0} = x⁰ = 1 (viii) 9⁵ x 3⁵ [since (a^mx b^m) = (a x b)^m] = (9 x 3)⁵ = 27⁵ (ix) 3^y x 12^y = (3 x 12)^y = 36^y (x) 25⁶ x 5⁶ = (25 x 5)⁶ = 125⁶

Simplify using laws of exponents.(i) 35 x 38(ii) a4 x a10(iii) 7x x 72(iv) 25 ÷ 23(v) 188 ÷ 184(vi) (64)3(vii) (xm)0(viii) 95 x 35(ix) 3y x 12y(x) 256 x 56

Answer»

(i) 3⁵ x 3⁸

[since a^m x aⁿ = a^{m + n}]

= 3^{5 + 8}

= 3¹³

(ii) a⁴ x a¹⁰

= a^{4 + 10}

= a¹⁴

(iii) 7^x x 7²= 7^{x + 2}

(iv) 2⁵ ÷ 2³

[since \(\frac{a^m}{a^n}\) = a^{m - n}]

= 2^{5 - 3}

= 2²

(v) 18⁸ ÷ 18⁴

= 18^{8 - 4}

= 18⁴

(vi) (6⁴)³

[since (a^m)ⁿ = a^{m x n}]

= 6^{4 x 3}

= 6¹²

(vii) (x^m)⁰

[since (a^m)ⁿ = a^{m x n}; a⁰ = 1]

= x^{m x 0}

= x⁰

= 1

(viii) 9⁵ x 3⁵

[since (a^mx b^m) = (a x b)^m]

= (9 x 3)⁵

= 27⁵

(ix) 3^y x 12^y

= (3 x 12)^y

= 36^y

(x) 25⁶ x 5⁶

= (25 x 5)⁶

= 125⁶