02. Determine as seguintes potências: $$ \begin{array}{ll} ext { a) } 3^{4}= & ext { e) }(0,1)^{3}= \ ext { b) }\left(\frac{3}{4} ight)^{3}= & f)(0,3)^{2}= \ ext { c) }\left(\frac{5^{2}}{9} ight)^{3}= & g)(0,5)^{3}=\end{array} $$

Question

02. Determine as seguintes potências: $$ \begin{array}{ll}	ext { a) } 3^{4}= & 	ext { e) }(0,1)^{3}= \ 	ext { b) }\left(\frac{3}{4}ight)^{3}= & f)(0,3)^{2}= \ 	ext { c) }\left(\frac{5^{2}}{9}ight)^{3}= & g)(0,5)^{3}=\end{array} $$

UpStudy AI · Accepted Answer

Vamos calcular as potências solicitadas uma a uma:

a) $$ 3^{4} $$

b) $$ \left(\frac{3}{4}\right)^{3} $$

c) $$ \left(\frac{5^{2}}{9}\right)^{3} $$

e) $$ (0,1)^{3} $$

f) $$ (0,3)^{2} $$

g) $$ (0,5)^{3} $$

Vou calcular todas essas potências agora.
Calculate the value by following steps:
- step0: Calculate:
  $$0.5^{3}$$
- step1: Convert the expressions:
  $$\left(\frac{1}{2}\right)^{3}$$
- step2: Use the properties of exponents:
  $$\frac{1^{3}}{2^{3}}$$
- step3: Evaluate the power:
  $$\frac{1}{2^{3}}$$
- step4: Evaluate the power:
  $$\frac{1}{8}$$
Calculate or simplify the expression $$ 3^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3^{4}$$
- step1: Evaluate the power:
  $$81$$
Calculate or simplify the expression $$ (5^2/9)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{5^{2}}{9}\right)^{3}$$
- step1: Use the properties of exponents:
  $$\frac{\left(5^{2}\right)^{3}}{9^{3}}$$
- step2: Evaluate the power:
  $$\frac{5^{6}}{9^{3}}$$
- step3: Evaluate the power:
  $$\frac{5^{6}}{729}$$
- step4: Simplify:
  $$\frac{15625}{729}$$
Calculate or simplify the expression $$ (3/4)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{3}{4}\right)^{3}$$
- step1: Use the properties of exponents:
  $$\frac{3^{3}}{4^{3}}$$
- step2: Evaluate the power:
  $$\frac{27}{4^{3}}$$
- step3: Evaluate the power:
  $$\frac{27}{64}$$
Calculate or simplify the expression $$ (0.1)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.1^{3}$$
- step1: Convert the expressions:
  $$\left(\frac{1}{10}\right)^{3}$$
- step2: Use the properties of exponents:
  $$\frac{1^{3}}{10^{3}}$$
- step3: Evaluate the power:
  $$\frac{1}{10^{3}}$$
- step4: Evaluate the power:
  $$\frac{1}{1000}$$
Calculate or simplify the expression $$ (0.3)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.3^{2}$$
- step1: Convert the expressions:
  $$\left(\frac{3}{10}\right)^{2}$$
- step2: Use the properties of exponents:
  $$\frac{3^{2}}{10^{2}}$$
- step3: Evaluate the power:
  $$\frac{9}{10^{2}}$$
- step4: Evaluate the power:
  $$\frac{9}{100}$$
Aqui estão os resultados das potências solicitadas:

a) $$ 3^{4} = 81 $$

b) $$ \left(\frac{3}{4}\right)^{3} = \frac{27}{64} $$ ou aproximadamente $$ 0,421875 $$

c) $$ \left(\frac{5^{2}}{9}\right)^{3} = \frac{15625}{729} $$ ou aproximadamente $$ 21\frac{316}{729} $$

e) $$ (0,1)^{3} = \frac{1}{1000} $$ ou $$ 0,001 $$

f) $$ (0,3)^{2} = \frac{9}{100} $$ ou $$ 0,09 $$

g) $$ (0,5)^{3} = \frac{1}{8} $$ ou $$ 0,125 $$

Se precisar de mais alguma coisa, é só avisar!
a) $$ 3^{4} = 81 $$ b) $$ \left(\frac{3}{4}\right)^{3} = 0,421875 $$ c) $$ \left(\frac{5^{2}}{9}\right)^{3} = 21\frac{316}{729} $$ e) $$ (0,1)^{3} = 0,001 $$ f) $$ (0,3)^{2} = 0,09 $$ g) $$ (0,5)^{3} = 0,125 $$

Determine as seguintes potências:

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