Mathematics, 29.08.2019 18:00, Jackson4568

Wat is the simplified expression for 3^-4 • 2^3 • 3^2 over 2^4 • 3^-3

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Answers

The answer is: " $\frac{3}{2}$ " .
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(or, write as: "1½" ; or, "1.5").
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Explanation:
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We are asked to simplify the given expression:
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→ $\frac{3^{-4}×2^{3}×3^{2} }{2^{4}×3^{-3}} 

$ ;
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Note: In the "numerator" :
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→  2³ = 2 × 2 × 2 = 8 .

→ 3² = 3 × 3 = 9 .
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Note: In the "denominator" :
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→ 2⁴ = 2 × 2 × 2 × 2 = 16 .
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So, rewrite our expression; substituting "8" for "(2³)";
and substituting "9" for "(3²)" — [in the numerator] ;
and substituting: "16" for "(2⁴)" — [in the denominator] ;
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→ AS FOLLOWS:
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→ $\frac{3^{-4}×2^{3}×3^{2} }{2^{4}×3^{-3}}$ ;

= $\frac{3^{-4}×8×(9}{16×3^{-3}}$ ;
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   → Since we have an "8" in the "numerator"; and a "16" in the "denominator" —respectively; and since both values, taken individually in the numerator—and taken individually in the denominator— are multiplied by other values as isolated numbers; we can "cancel out" the "8" in the "numerator" to a "1"; and change the "16" in the "denominator" to a "2" ; since:
"16÷8 = 2" ; and since "8÷8=1" ; that is: "8/16 = 1/2". We can then "eliminate" the "1" in the "numerator"; since in the numerator, there are other values that are multiplied by this "1" ; & any value multiplied by "1" is equal to that same value.
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So we can rewrite the expression, as follows:
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→ $\frac{3^{-4}×(9)}{2×3^{-3}}$ ;

↔ Rearrange and rewrite as follows:
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→ $\frac{3^{-4}×(9)}{2×3^{-3}}$

= $\frac{(9) *{3^{-4}}{2×3^{-3}}$ ;
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→ Note the following properties of exponents:
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⇒ ( $\frac{a} {b}$ ⁿ = $\frac{ a^{n}}{b^{n}}$ ;
  → (b ≠ 0) ;
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⇒ ( $a^{m}$ )ⁿ = a $a^{(m*n)}}$ ;
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⇒ $a^{m} a^{n} = a^{(m+n)}$ ;

and especially:

⇒ $\frac{ a^{m}}{ a^{n}} = a^{(m-n)} ; (a \neq 0) ;$ ;

and especially:

⇒ $a^{-n} = \frac{1}{(a^{n) }}$ ; (a $\neq 0);$ ); If "n" is a positive integer; and if "a" is a non-zero real number.
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→ So; (3⁻⁴) / (3⁻³) = 3⁽⁽⁻⁴ ⁻ ⁽⁻³⁾⁾ = 3⁽⁻⁴ ⁺ ³⁾ = 3⁻¹
= $\frac{1}{(3^{1})} = \frac{1}{3} ;$ ;
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→ Rewrite the expression:
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→ $\frac{(9) *{3^{-4}}{2×3^{-3}}$ ;

= $\frac{(9*1)}{(2*3)} ; = \frac{9}{6} ; = \frac{(9/3) }{(6/3)} ; = \frac{3}{2}$ ; or; write as: " 1 ½ " ; or, write as: " 1.5 ".
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answered: Guest

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

answered: Guest

5x+10 is the correct one

hope this