Question

Evaluate each exponential expression.

Answer 1

Explanation:

`(a^(m))/(a^(n))=a^(m-n),m>n\\\\\\(a^(m))/(a^(n))=(1)/(a^(m-n)), m<n`

`(5x^(4)y^(7))/(25xy^(10))=(5x^(4)y^(7))/(5^(2)xy^(10))\\\\=(x^(4-1))/(5^(2-1)*y^(10-7))\\\\=(x^(3))/(5y^(3))`

2)
`a^(m)*a^(n)=a^(m+n)`

`(-3x^(3)y^(5))(5xy^(-3))= -3*5 *x^(3+1)*y^(5-3)\\\\= -15x^(4)y^(2)`

3)
`a^(-m)=(1)/(a^(m))`

`(24a^(4)b^(-3))/(16a^(-2)b)=(3a^(4)b^(-3))/(2a^(-2)b)\\\\=\frac{3a^{4*a^(2)}}{2a^(-2)*b*b^(3)}\\\\=(3a^(4+2))/(2b^(1+3))\\\\=(3a^(6))/(2b^(4))`