Understand the problem: Understand the problem. We need to find the value of raising the fraction 1/6 to the power of -3. A negative exponent indicates that we should take the reciprocal of the base and then raise it to the absolute value of the exponent.Apply the negative exponent rule: Apply the negative exponent rule. (1/6)^-3 means we take the reciprocal of 1/6 and raise it to the power of 3. Reciprocal of 1/6 is 6/1, which is simply 6. So, (1/6)^-3 = (6/1)^3Calculate the value: Calculate the value of (6/1)^3. Now we raise 6 to the power of 3. (6/1)^3 = 6^3 = 6 * 6 * 6Perform the multiplication: Perform the multiplication. 6 * 6 * 6 = 36 * 6 = 216 So, (6/1)^3 = 216

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$\left(\frac{1}{6}\right)^{-3}$

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Algebra 2

Add, subtract, multiply, and divide polynomials

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\left(\frac{1}{6}\right)^{-3}

Understand the problem: Understand the problem. $\newline$ We need to find the value of raising the fraction $\frac{1}{6}$ to the power of $-3$ . A negative exponent indicates that we should take the reciprocal of the base and then raise it to the absolute value of the exponent.
Apply the negative exponent rule: Apply the negative exponent rule. $\newline$ $(1/6)^{-3}$ means we take the reciprocal of $1/6$ and raise it to the power of $3$ . $\newline$ Reciprocal of $1/6$ is $6/1$ , which is simply $6$ . $\newline$ So, $(1/6)^{-3} = (6/1)^3$
Calculate the value: Calculate the value of $(\frac{6}{1})^3$ . Now we raise $6$ to the power of $3$ . $(\frac{6}{1})^3 = 6^3 = 6 \times 6 \times 6$
Perform the multiplication: Perform the multiplication. $\newline$ $6 \times 6 \times 6 = 36 \times 6 = 216$ $\newline$ So, $(6/1)^3 = 216$