When do you add exponents?

The rules for exponents are

Multiplication;

a^(n) X a^(m) = a^(n+m)

Notice the coefficient 'a' MUST be the same for addition of exponents.

For something like

a^(n) X b^(m) you CANNOT add the exponents, because the coefficients are different. 'a' & 'b'

Division

a^(n) / a^(m) = a^(n-m) Subtract the exponents)

Nesting

(a^(n))^(m) = a^(nm) (Multiply the exponents).

However, in all Cases the coefficient MUST be the same .e.g. 'a'.

e.g.

3^(2) X 3^(5) = 3^(7)

5^(3) divide 5^(2) = 5^(1) = 5

(7^(3))^4) = 7^(12)

However,

3^(2) X 5^(3) = NOT allowed. because 9 x 125 = 1125 Not equal to the sqyare root or cube root of either number.

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