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max2010maxim [7]
3 years ago
8

HELP PLEASE i dont understand at all...

Mathematics
1 answer:
bija089 [108]3 years ago
8 0

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.

\dfrac{x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=\dfrac{x^{5}}{x^{3}}\\\\=\dfrac{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.

\dfrac{x\cdot x\cdot x}{x\cdot x\cdot x\cdot x\cdot x}=\dfrac{x^{3}}{x^{5}}=\dfrac{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:

\dfrac{1}{3^{-2}}=3^{2}\\\\=3\cdot 3=\bf{9}

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