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lina2011 [118]
2 years ago
6

Mathematics 13 don’t understand

Mathematics
1 answer:
UNO [17]2 years ago
6 0

Answer:

  1/6^3

Step-by-step explanation:

The applicable rules of exponents are ...

  a^-b = 1/a^b

  (a^b)(a^c) = a^(b+c)

__

Your expression can be simplified as follows:

  \dfrac{6^{-5}}{6^{-2}}=\dfrac{1}{(6^{-2})(6^5)}=\dfrac{1}{6^{-2+5}}=\boxed{\dfrac{1}{6^3}}

_____

<em>Additional comment</em>

If you think of an exponent as signifying repeated multiplication, the rules of exponents may be easier to remember. The exponent tells you how many times the base is a factor in the product.

Consider multiplication:

  (x\cdot x\cdot x)\cdot(x\cdot x)=x^3\cdot x^2=x^{3+2}=x^5\\\\(x\cdot x\cdot x)\cdot(x\cdot x\cdot x)=(x^3)^2=x^{3\cdot2}=x^6

Consider division:

  \dfrac{x\cdot x\cdot x}{x\cdot x}=x\quad\Longleftrightarrow\quad\dfrac{x^3}{x^2}=x^{3-2}=x^1\\\\\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{1}{x}\quad\Longleftrightarrow\quad\dfrac{x^2}{x^3}=x^{2-3}=x^{-1}

This may help you see that a positive exponent in the denominator is equivalent to a negative exponent in the numerator (and vice versa).

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