Identify base and exponent: Identify the base and the exponent. In the expression ((1)/(5))^(-3), (1/5) is the base raised to the exponent -3. Base: 1/5 Exponent: -3Understand negative exponent rule: Understand the negative exponent rule. A negative exponent means that we take the reciprocal of the base and change the sign of the exponent to positive. So, ((1)/(5))^(-3) means we take the reciprocal of 1/5 and raise it to the power of 3. Reciprocal of 1/5: 5/1 or simply 5Apply negative exponent rule: Apply the negative exponent rule. ((1)/(5))^(-3) becomes (5/1)^3.Calculate value of (5/1)^3: Calculate the value of (5/1)^3. (5/1)^3 means 5 is multiplied by itself 3 times. (5/1)^3 = 5 × 5 × 5Perform multiplication: Perform the multiplication. 5 × 5 × 5 = 125Write final answer: Write the final answer. The value of ((1)/(5))^(-3) is 125.

Grade 8

Powers with negative bases

Full solution

\left(\frac{1}{5}\right)^{-3}=

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $\left(\frac{1}{5}\right)^{-3}$ , $\left(\frac{1}{5}\right)$ is the base raised to the exponent $-3$ . $\newline$ Base: $\frac{1}{5}$ $\newline$ Exponent: $-3$
Understand negative exponent rule: Understand the negative exponent rule. A negative exponent means that we take the reciprocal of the base and change the sign of the exponent to positive. So, $(\frac{1}{5})^{-3}$ means we take the reciprocal of $\frac{1}{5}$ and raise it to the power of $3$ . Reciprocal of $\frac{1}{5}$ : $\frac{5}{1}$ or simply $5$
Apply negative exponent rule: Apply the negative exponent rule. $\newline$ $(\frac{1}{5})^{-3}$ becomes $(\frac{5}{1})^3$ .
Calculate value of $(5/1)^3$ : Calculate the value of $(5/1)^3$ . $(5/1)^3$ means $5$ is multiplied by itself $3$ times. $(5/1)^3 = 5 \times 5 \times 5$
Perform multiplication: Perform the multiplication. $5 \times 5 \times 5 = 125$
Write final answer: Write the final answer. $\newline$ The value of $\left(\frac{1}{5}\right)^{-3}$ is $125$ .