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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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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Answer from: Quest

What are the options

Answer from: Quest

idk

step-by-step explanation:

58.35 what is the volume of the can below? use - 3.14 and round your answer to the nearest tenth. 8

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