TICE es $\newline$ $4$ $\newline$ If $c=b^{-3}$ , what is $b$ in terms of $c$ ? $\newline$ A. $c^{\frac{1}{3}}$ $\newline$ B. $c^{3}$ $\newline$ C. $\frac{1}{c^{3}}$ $\newline$ D. $\frac{1}{\sqrt[3]{c}}$

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Algebra 2

Simplify expressions using trigonometric identities

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Q. TICE es

\newline

4

\newline

c=b^{-3}

, what is

b

in terms of

c

\newline

c^{\frac{1}{3}}

\newline

c^{3}

\newline

\frac{1}{c^{3}}

\newline

\frac{1}{\sqrt[3]{c}}

Take Cube Root: Express the given equation $c = b^{-3}$ in a form that isolates $b$ . To do this, we need to take the cube root of both sides of the equation to get rid of the exponent of $-3$ .
Simplify Exponents: Taking the cube root of both sides gives us the cube root of $c$ equals the cube root of $b^{-3}$ , which can be written as $c^{\frac{1}{3}} = (b^{-3})^{\frac{1}{3}}$ .
Reciprocal of Both Sides: Simplify the right side of the equation by multiplying the exponents. The cube root is the same as raising to the power of $\frac{1}{3}$ , so we have $(b^{-3})^{\frac{1}{3}} = b^{-3 \times \frac{1}{3}} = b^{-1}$ .
Express in Different Form: Since $b^{-1}$ is the same as $\frac{1}{b}$ , we can write the equation as $c^{\frac{1}{3}} = \frac{1}{b}$ . To solve for $b$ , we take the reciprocal of both sides, which gives us $b = \frac{1}{c^{\frac{1}{3}}}$ .
Rewrite as Cube Root: Recognize that $1/(c^{1/3})$ is the same as $c$ raised to the power of negative one-third, which can be written as $b = c^{-1/3}$ . However, this is not one of the options provided in the multiple-choice answers. We need to express it in a form that matches one of the options.
Rewrite as Cube Root: Recognize that $1/(c^{1/3})$ is the same as $c$ raised to the power of negative one-third, which can be written as $b = c^{-1/3}$ . However, this is not one of the options provided in the multiple-choice answers. We need to express it in a form that matches one of the options.We can rewrite $c^{-1/3}$ as the cube root of $1/c$ , which is the same as the reciprocal of the cube root of $c$ . This matches option D: $b = 1/\sqrt[3]{c}$ .