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ivanzaharov [21]

3 years ago

7

Ginger wants to join a gym. She goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthl

y fee of $30. What algebraic expression represents the total cost of joining the gym?

1 answer:

AysviL [449]3 years ago

5 0

100+30(n) n being the amount of months

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Write the expression using rational exponents. Then simplify and convert back to radical notation.

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Answer:

The radical notation is $3x\sqrt[3]{y^2z}$

Step-by-step explanation:

Given

$\sqrt[3]{27 x^{3} y^{2} z}$

Step 1 of 1

Write the expression using rational exponents.

$\sqrt[n]{a^{m}}=\left(a^{m}\right)^{\frac{1}{n}}$

$=a^{\frac{m}{n}}:\left({27 x^{3} y^{2} z})^{\frac{1}{3}}$

$(a \cdot b)^{r}=a^{r} \cdot b^{r}:(27)^{\frac{1}{3}}\left(x^{3}\right)^{\frac{1}{3}} \cdot\left(y^{2}\right)^{\frac{1}{3}} \cdot(z)^{\frac{1}{3}}$

$=$(3^3)^{\frac{1}{3}}\left(x^{3}\right)^{\frac{1}{3}} \cdot\left(y^{2}\right)^{\frac{1}{3}} \cdot(z)^{\frac{1}{3}}$$

$=\left(3\right)\left(x}\right)} \cdot\left(y}\right)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

$=3x \cdot(y)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

Simplify $3 x \cdot(y)^{\frac{2}{3}} \cdot(z)^{\frac{1}{3}}$

$=3 x \sqrt[3]{y^{2} z}$

Learn more about radical notation, refer :

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