Simplification of Exponents

Example 1: Simplify 32 x 33 Solution: 32 x 33 . Here we have same base 3. By applying the product rule, am x an = am+n 32 x 33 = 32+3 = 35 = 243 Example 2: 63 x 53 63 x 53 . Here we have same power 3. By applying the same power rule, am x bm = (a x b)m 63 x 53 = (6 x 5)3 (6 x 5)3 = 303 = 27000

Example 3: Simplify 105 ÷ 102 Solution: Here we have same base 10. By applying the quotient rule, am ÷ an = am-n 105 ÷ 102 = 105-2 = 103 = 1000 Example 4: Simplify By applying Power of quotient rule,

Example 5: Simplify (43)2 Solution: By applying power rule , (am)n = am x n (43)2 = 43 x 2 = 46 = 4096 (46 = 4 X 4 X 4 X 4 X 4 X 4 = 4096) Example 6: Simplify (34)0 Here we have to multiply the powers, (am)n = am x n (34)0 = 34 x 0 = 30 = 1 (any number raised to the power 0 is 1, a0 = 1)

Example 7: Solution = 1 (By applying number with zero exponent a0=1 ) Observe the product of first two exponents, they have same base and we can apply product rule (By applying Quotient rule = 1 (By applying number with zero exponent a0=1 )

Example 8: 10-4 Solution: Example 9: (6 x 5)3 Solution: We know that by law of reciprocal a-m= Example 9: (6 x 5)3 Solution: There is no rule applied here. Find the product first and then find exponent. (6 x 5)3 = 303 = 27000

Example 10: Solution: ( By using power rule )

Example 11: Solution: ( By using power rule

=3-6+4 x 2-6+8 x 42 (By applying the Product rule in Cont…… (By using reciprocal rule) =3-6 x 2-6 x 28 x 34 x 42 =3-6 x 34 x 2-6 x 28 x 42 (Grouping the exponents based on their bases) =3-6+4 x 2-6+8 x 42 (By applying the Product rule in =3-2 x 22 x 42 ( After applying integer rule) (By using reciprocal rule )

Try these Simplify: 23 x 25 b) 46÷43 c) d) (93)0 Solve: