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Extension
Writs a question that could give an answer of
(a^(3)b^(-3))/(c^(3))

Extension $\newline$ Writs a question that could give an answer of $\frac{a^{3} b^{-3}}{c^{3}}$

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Evaluate rational exponents

Full solution

Q. Extension

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Writs a question that could give an answer of

\frac{a^{3} b^{-3}}{c^{3}}

Given Expression: Let's start with the given expression $\frac{a^{3}b^{-3}}{c^{3}}$ .
Create Fraction: We need to create a problem that simplifies to this expression. Let's think of a fraction that involves $a$ , $b$ , and $c$ raised to powers.
Cube Root Simplification: How about we start with $(a^6b^{-2})/(c^6)$ ? If we take the cube root of this, it should simplify to our target expression.
Exponent Property: So, the cube root of $(a^6b^{-2})/(c^6)$ is $((a^6b^{-2})/(c^6))^{1/3}$ .
Simplify Exponents: Using the property of exponents that says $x^{\frac{m}{n}} = (x^m)^{\frac{1}{n}}$ , we can rewrite this as $\frac{a^{6\cdot\frac{1}{3}}b^{-2\cdot\frac{1}{3}}}{c^{6\cdot\frac{1}{3}}}$ .
Simplify Exponents: Using the property of exponents that says $x^{\frac{m}{n}} = (x^m)^{\frac{1}{n}}$ , we can rewrite this as $\frac{a^{6\cdot(\frac{1}{3})}b^{-2\cdot(\frac{1}{3})}}{c^{6\cdot(\frac{1}{3})}}$ . Simplify the exponents by multiplying: $a^{\frac{6}{3}} = a^2$ , $b^{-\frac{2}{3}}$ , and $c^{\frac{6}{3}} = c^2$ .

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f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}

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We want to find

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What happens when we use direct substitution?

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(A) The limit exists, and we found it!

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(B) The limit doesn't exist (probably an asymptote).

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(C) The result is indeterminate.

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