Question

Find the value of 〖32〗^0.8 . ​

Answer 1

$\implies {32}^{0.8} = 16.319$

Hope it helps you...

Answer 2

The answer is 16.

GIVEN

Mathematical expression;

$(32)^{0.8}$

TO FIND

The value of given expression

SOLUTION

We can simply solve the above problem as follows;

We are given,

$(32)^{0.8}$

We can observe that the exponent is in the decimal form.

Converting the decimal exponent into fractional exponent.

0.8 = 8/10

Simplifying the fraction;

8/10 = 4/5

Now,

We can write the base (32) as

32 = 2×2×2×2×2 = 2⁵

Now,

$(32)^{0.8} = ( {2}^{5} )^{ \frac{4}{ 5} }$

We know that,

(aⁿ)ᵐ = (a)ⁿˣᵐ

Therefore,

$( {2}^{5} )^{ \frac{4}{ 5} } = {2}^{5 \times \frac{4}{5} }$

Solving the exponent;

5 × 4/5 = 4

2⁴ = 2×2×2×2 = 16

Hence, The answer is 16.

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