1.  Using laws of exponents, simplify and write the answer in exponential form:

           (i)\: 3^{2}\times 3^{4}\times 3^{8}             (ii)\: 6^{15}\div 6^{10}        (iii)\: a^{3}\times a^{2}         (iv)\: 7^{x}\times 7^{2}

            (v)\:(5^{2})^{3}\div 5^{3}                  (vi)\:2^{5}\times 5^{5}           (vii)\:a^{4}\times b^{4}         (viii)\:(3^{4})^{3}

           (ix)\:(2^{20}\div 2^{15})\times 2^{3}        (x)\:8^{t}\div 8^{2}

Answers (1)
M mansi

  (i)\: 3^{2}\times 3^{4}\times 3^{8}      

can be simplified as 3^{(2+4+8)}=3^{14}

  (ii)\: 6^{15}\div 6^{10}       

can be simplified as 6^{(15-10)}=6^{5}

(iii)\: a^{3}\times a^{2}

can be simplified as      a^{(3+2)}=a^{5}  

(iv)\: 7^{x}\times 7^{2}

can be simplified as 7^{(x+2)}=7^{(x+2)}

 (v)\:(5^{2})^{3}\div 5^{3}

can be simplified as  5^{(2\times 3)}\div 5^{(3)}=5^6\div 5^3=5^{6-3}=5^3                

(vi)\:2^{5}\times 5^{5}         

can be simplified as  

(2\times5)^{5}=10^5

(vii)\:a^{4}\times b^{4}       

can be simplified as  (ab)^4

(viii)\:(3^{4})^{3}

can be simplified as 3^{4\times 3}=3^{12}

 (ix)\:(2^{20}\div 2^{15})\times 2^{3}

can be simplified as     2^{(20-15)}\times 2^3=2^5\times 2^3=2^{(5+3)}=2^8    

(x)\:8^{t}\div 8^{2}

can be simplified as 8^{(t-2)}

Preparation Products

Knockout KCET 2021

An exhaustive E-learning program for the complete preparation of KCET exam..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout KCET JEE Main 2021

It is an exhaustive preparation module made exclusively for cracking JEE & KCET.

₹ 27999/- ₹ 16999/-
Buy Now
Knockout NEET Sept 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
Buy Now
Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
Buy Now
Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Exams
Articles
Questions