Question

Why is 3 squre root 4 equal to 4⅓

Answer 1

3 square root of 4 is equal to $4^{1/3}$ using the fractional exponent rule.

The exponents are a way of representing numbers in the form aⁿ, which is read as a to the power of n, and its value is derived by multiplying a with itself n number of times.

The application of exponents follow some laws or rules, which can be shown as follows:

• Product of power rule: $a^m * a^n = a^{m+n}$
• Quotient of power rule: $a^m \div a^n = a^{m-n}$
• Power of a power rule: $(a^m)^n = a^{mn}$
• Power of product rule: $(ab)^m = a^m * b^m$
• Power of quotient rule: $(a/b)^m = a^m/b^m$
• Zero power rule: $a^0 = 1$
• Negative Exponent rule: $a^{-n} = 1/a^n$
• Fractional exponent rule: $\sqrt[n]{a} = a^{1/n}$

In the question, we are asked why is 3 square root 4 equal to $4^{1/3}$.

The expression "3 square root of 4" is actually cube root of 4, written as ∛4.

Using the fractional exponent rule, according to which $\sqrt[n]{a} = a^{1/n}$, we can write ∛4 as  $4^{1/3}$.

Thus, 3 square root of 4 is equal to $4^{1/3}$ using the fractional exponent rule.

Learn more about the rules of exponents at

https://brainly.com/question/847241

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