Question

The value of (125)power of 1/3 is ___
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Answer 1

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Answer:

The value of 125 power of 1/3 is 5.

Step-by-step explanation:

${125}^{ \frac{1}{3} } = \sqrt[3]{125}$

$= \sqrt[3]{ {5}^{3} } = 5$

Answer 2

Answer:

The value of (125)power of 1/3 is 5.

Step-by-step explanation:

Step 1: Exponent rules are the laws that are applied to simplify exponent-based expressions. The principles of exponents make it simple to carry out several mathematical operations, such as addition, subtraction, multiplication, and division, in a short amount of time. Additionally, these principles aid in the simplification of numbers with complicated powers incorporating roots, fractions, and decimals.

Step 2: Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.

$125^{\frac{1}{3}}$

Factor the number: $125=5^3$

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

Step 3:Apply exponent rule: $\quad\left(a^b\right)^c=a^{b c}, \quad a \geq 0$

$=5^{3 \cdot \frac{1}{3}}$

$\begin{aligned}& 3 \cdot \frac{1}{3}=1 \\& =5^{-1}\end{aligned}$

Apply exponent rule: $a^1=a^{-0$

=5

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