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lisabon 2012 [21]
2 years ago
13

Help I can’t get this ! Please help

Mathematics
1 answer:
Zielflug [23.3K]2 years ago
8 0

Answer:

\sqrt{2^5}

Step-by-step explanation:

First, deal with the product of the two powers of 2 inside the parentheses.

The two factors are powers of 2, so add the exponents.

(2^{\frac{1}{2}} \cdot 2^{\frac{3}{4}})^2 =

= (2^{\frac{1}{2} + \frac{3}{4}})^2

You need a common denominator, 4, to add the fractions.

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

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

Now you have an exponent raised to an exponent. Multiply the exponents and reduce the fraction.

= 2^{\frac{5}{4} \times 2}

= 2^{\frac{10}{4}}

= 2^{\frac{5}{2}}

When a fraction is an exponent, the numerator is an exponent and the denominator is the index of the root. A denominator of 2 means a root index of 2 which means square root.

= \sqrt{2^5}

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