<s>[INST] What is the actual meaning of power which is less than 1? $3^4 = 3 \cdot 3 \cdot 3 \cdot 3$
$3^2 = 3 \cdot 3$
$3^1 = 3$
But my problem is for below 1:
Example:
$3^{0.7} = \ ?$
Can you please explain it to clear my doubt? 
 [/INST] Exponents less than 1 are better understood in terms of fractions rather than decimals:
$3^4=3^{2+2}=3^2•3^2$
Therefore:
$3^1=3^{\frac{1}{2}+\frac{1}{2}}=3^\frac{1}{2}•3^\frac{1}{2}=(3^\frac{1}{2})^2$
What value, when multiplied by itself, is equal to 3? The only possibility is ±$\sqrt{3}$. This is why we understand an exponent of $\frac{1}{2}$ to be equivalent to the square root. Similarly, an exponent of $\frac{1}{3}$ is the cube root. Any value in the numerator is the equivalent of an integer exponent.
To determine the value of $3^{0.7}$, convert the exponent to a fraction: $0.7=\frac{7}{10}$. So $3^{0.7}=3^\frac{7}{10}=(3^7)^{1/10}=\sqrt[10]{3^7}≈2.16$.
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