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SashulF [63]
3 years ago
6

Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64

Mathematics
2 answers:
Crazy boy [7]3 years ago
7 0

Answer:

Option B is correct that is 8.

Step-by-step explanation:

Given Expression : (16^{\frac{3}{2}})^{\frac{1}{2}}

We use a law of exponent here to simplify it,

(x^a)^b=x^{ab}

Consider,

(16^{\frac{3}{2}})^{\frac{1}{2}}

=16^{\frac{3}{2}\times\frac{1}{2}}

=16^{\frac{3}{4}}

=(2^4)^{\frac{3}{4}}

=2^{4\times\frac{3}{4}}

=2^3

=8

Therefore, Option B is correct that is 8.

Pani-rosa [81]3 years ago
6 0
\bf a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\
\left( 16^{\frac{3}{2}} \right)^{\frac{1}{2}}\implies 16^{\frac{3}{2}\cdot \frac{1}{2}}\implies 16^{\frac{3}{4}}\qquad \boxed{16=2^4}\qquad (2^4)^{\frac{3}{4}}\implies 2^{4\cdot \frac{3}{4}}
\\\\\\
2^3\implies 8
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