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(50 points) EXPRESS AS A POWER OF 3, Please explain your work
do a, b, and c
don’t troll or steal answers, i searched the answers up but nothing popped up :/

50 Points EXPRESS AS A POWER OF 3 Please Explain Your Work Do A B And C Dont Troll Or Steal Answers I Searched The Answers Up But Nothing Popped Up class=

Sagot :

Semsee45idn

Answer:

[tex]\textsf{(a)} \quad 3^{-2}[/tex]

[tex]\textsf{(b)} \quad 3^{-5}[/tex]

[tex]\textsf{(c)} \quad 3^{9}[/tex]

Step-by-step explanation:

Part (a)

Given:

[tex]\dfrac{1}{9}[/tex]

Rewrite 9 as 3²:

[tex]\implies \dfrac{1}{3^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}:[/tex]

[tex]\implies 3^{-2}[/tex]

Part (b)

Given:

[tex]\dfrac{3^{-4} \cdot 3^2}{3^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{3^{(-4+2)}}{3^3}[/tex]

[tex]\implies \dfrac{3^{-2}}{3^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 3^{(-2-3)}[/tex]

[tex]\implies 3^{-5}[/tex]

Part (c)

Given:

[tex]27^2 \div 3^{-3}[/tex]

Rewrite 27 as 3³:

[tex]\implies (3^3)^2 \div 3^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^6 \div 3^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]

[tex]\implies 3^{(6-(-3))}[/tex]

[tex]\implies 3^{(6+3)}[/tex]

[tex]\implies 3^9[/tex]

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