Respuesta :

AadhPrit

Answer:

The answers of the questions are given below :

  • a) = 4096
  • b) = 1.25
  • 3) = m²
  • 4) = r⁴s³
  • 5) = a⁸/b¹²

Step-by-step explanation:

[tex]\large{\tt{\underline{\underline{\red{QUESTION}}}}}[/tex]

[tex]\begin{gathered}\footnotesize\boxed{\begin{array}{c|c|c}\bf\underline{Given}&\bf\underline{Solution}&\bf{\underline{Simple\: Form}}\\\\\rule{60pt}{0.5pt} &\rule{70pt}{0.5pt}& \rule{70pt}{0.5pt}\\\\ 1.\: {4}^{6} & & \\\\ 2.\: \bigg(\dfrac{2^6}{5^3} \bigg)& &\\\\ 3. \: \Big({m}^{\frac{2}{3}}\Big)\bull \Big({m}^{\frac{4}{3}}\Big) & &\\\\4. \: \big({r}^{12} {s}^{9}\big)^{ - \frac{1}{3}} &&\\\\ 5.\bigg(\dfrac{a^4}{a^6}\bigg)^{2}& &\end{array}}\end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\large{\tt{\underline{\underline{\red{SOLUTION}}}}}[/tex]

Question. 1

>> 4⁶

[tex]\begin{gathered}\qquad{= 4 \times 4 \times 4 \times 4 \times 4 \times 4} \\ \qquad{= 16 \times 4 \times 4 \times 4 \times 4} \\ \qquad{= 64 \times 4 \times 4 \times 4} \\ \qquad{= 256\times 4 \times 4} \\ \qquad{= 1024 \times 4} \\ \qquad{= 4096} \end{gathered}[/tex]

  • Hence, the answer is 4096.

[tex]\begin{gathered}\end{gathered}[/tex]

Question. 2

>> (2⁶/5³)^-⅓

[tex]\begin{gathered} \qquad\implies{\bigg(\frac{2^6}{5^3}\bigg)^{ - \frac{1}{3}}}\\ \\ \qquad\implies{\bigg(\frac{64}{125}\bigg)^{ - \frac{1}{3}}}\\ \\\qquad\implies{\bigg( \frac{1}{\frac{64}{125}}\bigg)^{ \frac{1}{3}}} \\ \\ \qquad\implies{\bigg( 1 \times \frac{125}{64} \bigg)^{ \frac{1}{3}}} \\ \\ \qquad\implies{\bigg( \frac{125}{64} \bigg)^{ \frac{1}{3}}} \\ \\\qquad\implies{\bigg( \sqrt[3]{ \frac{125}{64}}\bigg)} \\ \\ \qquad\implies{\bigg( \dfrac{5}{4} \bigg)} \\ \\ \qquad\implies{\Big( 1.25\Big)}\end{gathered}[/tex]

  • Hence, the answer is 1.25.

[tex]\begin{gathered}\end{gathered}[/tex]

Question. 3

>> (m^2/3)•(m^4/3)

[tex]\begin{gathered} \qquad{= \Big({m}^{\frac{2}{3}}\Big) \bull \Big({m}^{ \frac{4}{3}}\Big)} \\ \\ \qquad{= \Big({m}^{\frac{2}{3} + \frac{4}{3}}\Big)} \\ \\ \qquad{= \Big({m}^{\frac{2 + 4}{3}}\Big)} \\ \\ \qquad{= \Big({m}^{\frac{6}{3}}\Big)} \\ \\ \qquad{= \Big({m}^{2}\Big)}\end{gathered}[/tex]

  • Hence, the answer is m².

[tex]\begin{gathered}\end{gathered}[/tex]

Question. 4

>> (r¹² s⁹)^⅓

[tex]\begin{gathered} \qquad\implies{\Big( {r}^{12} \: {s}^{9}\Big)^{\frac{1}{3}}}\\\\ \qquad\implies{\Big({r}^{\frac{12}{3} } \: {s}^{\frac{9}{3}}\Big)} \\ \\ \qquad\implies{\Big({r}^{\cancel{\frac{12}{3}}} \: {s}^{\cancel{\frac{9}{3}}}\Big)} \\ \\ \qquad\implies{\Big({r}^{4} \: {s}^{3}\Big)} \end{gathered}[/tex]

  • Hence, the answer is r⁴s³.

[tex]\begin{gathered}\end{gathered}[/tex]

Question. 5

>> (a⁴/b⁶)^2

[tex]\begin{gathered} \qquad{ = \Big(\frac{a^4}{b^6}\Big)^{2}} \\ \\ \qquad{ = \Big(\frac{a^{4 \times 2}}{b^{6 \times 2}}\Big)} \\ \\ \qquad{ = \Big(\frac{a^{8}}{b^{12}}\Big)} \end{gathered}[/tex]

  • Hence, the answer is a⁸/b¹².

[tex]\underline{\rule{220pt}{3pt}}[/tex]

akposevictor

Applying the rules of exponents the solutions in their simplest form are:

1. 4,096

2. 5/4

3. m²

4. [tex]\mathbf{ r^4s^3}[/tex]

5. [tex]\mathbf{ \frac{a^8}{b^{12}} }[/tex]

Rule of Exponents

1. [tex]a^3 = a \times a \times a[/tex]

2. [tex](a^mb^n)^p = a^{mp}b^{nP }[/tex]

3. [tex]a^n \times a^m = a^{(n + m)}[/tex]

4. [tex]a^{-n} = \frac{n}{a}[/tex]

Using the rules of exponents, find the solution of the given problem:

1. [tex]4^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex] = 4,096.

2. [tex]\frac{2^6}{5^3} ^{-\frac{1}{3}[/tex]

Apply the rule stated in number 1.

[tex](\frac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{5 \times 5 \times 5} )^{-\frac{1}{3}\\\\[/tex]

[tex](\frac{64}{125} )^{-\frac{1}{3}[/tex]

Apply the rule in number 4

[tex](\frac{1}{\frac{64}{125} } )^{\frac{1}{3}\\\\[/tex]

[tex]\sqrt[3]{\frac{125}{64} } \\\\\mathbf{\frac{5}{4} }[/tex]

3. [tex]m^{\frac{2}{3}} \times m^{\frac{4}{3}\\\\[/tex]

Apply the rule in number 3

[tex]m^{\frac{2}{3} + \frac{4}{3}\\\\[/tex]

= m²

4. [tex](r^{12} S^9)^{\frac{1}{3}[/tex]

Apply the rule in number 2.

[tex](r^{12 \times \frac{1}{3}} S^{9 \times \frac{1}{3}})\\\\\mathbf{= r^4s^3}[/tex]

5. [tex](\frac{a^4}{b^6} )^2[/tex]

Apply the rule in number 2.

[tex]\frac{a^{4 \times 2}}{b^{6 \times 2}} \\\\\mathbf{= \frac{a^8}{b^{12}} }[/tex]

Learn more about rules of exponents on:

https://brainly.com/question/12140519