To solve (3^3 \times 3^2), you can use the property of exponents that states (a^m \times a^n = a^{m+n}). Therefore, (3^3 \times 3^2 = 3^{3+2} = 3^5). Calculating (3^5) gives you (243).
(5*103)+(3*102) = 5300
729
(2)3 x (2)2 = 2(3+2) = (2)5 (8) x (4) = 32
multiplying a number by itself is a power 2^2=2 to the 2nd power 2^3=2 to the 3rd power
27/9
43 times 32 = 576
(5*103)+(3*102) = 5300
As a product of its prime factors in exponents: 23*32 = 72
729
(2)3 x (2)2 = 2(3+2) = (2)5 (8) x (4) = 32
multiplying a number by itself is a power 2^2=2 to the 2nd power 2^3=2 to the 3rd power
27/9
3 to the 2nd power times 3 to the 5th power = 3x3 x 3x3x3x3x3 = 2187
(3^2)^3 is 3^()2x3=3^6
3^(7) X 3^(3) = 3^(7 + 3) = 3^(10) The rules for For manipulating indices are . #1 ; The coefficient MUST always be the same '3' in the above case. #2 ; For Multiplication , you ADD the indices. #3 ; For Division you subtract the indices. #4 ; For 'nesting' you multiply the indices. Using the above data. Multiplication / Addition already done!!!! Division/subtraction 3^(10) divide 3^(3) = 3^(10 - 3) = 3^(7) 'Nesting' [ 3^(10) ] ^(3) = 3^(10 x 3) = 3^(30) These are algebraically expressed as a^(m) X a^(n) = a^(m+n) a^(m) / a^(n) = a^(m-n) [a^(m)]^(n) = a^(mn). NB Finally, you cannot do a^(m) X b^(n) is not equal to [ab]^(m+n). , because the coefficient 'a' & 'b' are different.
168
120