Question

HELP PLEASE

i dont understand at all...

Answer 1

An exponent signifies repeated multiplication.

`x\cdot x\cdot x=x^(3)` the factor x is repeated 3 times

Exponents can be added and subtracted to express the effects of multiplication and division.

`(x\cdot x\cdot x\cdot x\cdot x)/(x\cdot x\cdot x)=(x^(5))/(x^(3))\\\\=(x\cdot x\cdot x)/(x\cdot x\cdot x)\cdot x\cdot x=x\cdot x\\\\=x^((5-3))=x^(2)`

The addition and subtraction of exponents works the same even when there are more denominator factors than numerator factors.

`(x\cdot x\cdot x)/(x\cdot x\cdot x\cdot x\cdot x)=(x^(3))/(x^(5))=(1)/(x^(2))\\\\=x^((3-5))=x^(-2)`

That is, a negative numerator exponent is the same as a positive denominator exponent and vice versa. You can move a factor with an exponent from denominator to numerator and change the sign of the exponent, and vice versa.

Your expression has 3 in the denominator with a negative exponent. It can be moved to the numerator and the exponent changed to positive:

`(1)/(3^(-2))=3^(2)\\\\=3\cdot 3=\bf{9}`