Question

Using laws of exponents, simplify and express in exponential form a) 3^ 5 × 10^3 × 25 × ^7 / 5^ 7 × 6^ 5 × ^4​

Answer 1

Solution 1:

(i) \left[a^m\times a^n=a^{m+n}\right][am×an=am+n]

\left[3^{2+4+8}\right][32+4+8]

3^{14}314

(ii) \left[a^m\div a^n=a^{m-n}\right][am÷an=am−n]

=\left[6^{15-10}\right]=[615−10]

=6^5=65

(iii) \left[a^m\times a^n=a^{m+n}\right][am×an=am+n]

=\left[a^{3+2}\right]=[a3+2]

=a^5=a5

(iv) \left[a^m\times a^n=a^{m+n}\right][am×an=am+n]

=\left[7^{x+2}\right]=[7x+2]

(v) \left[\left(a^m\right)^n=a^{mn}\right][(am)n=amn]

=5^6\div5^3=56÷53

=5^3=53

(vi) a^m\times b^{m\ }=\left(a\times b\right)^mam×bm =(a×b)m

\left[2\times5\right]^5[2×5]5

\left[10\right]^5[10]5

(vii) a^m\times b^{m\ }=\left(a\times b\right)^mam×bm =(a×b)m