"How to simplify (81)34?" was answered by our experts

Secondary
Algebra
Pre-Algebra
Factors and multiples

Franco Avila

Answered question

2023-03-11

How to simplify

{(81)}^{\frac{3}{4}}

Answer & Explanation

Paxton Houston

Beginner2023-03-12Added 5 answers

Step

1

:We need find factors of

81

81

can be written as:

81 = 3 \times 3 \times 3 \times 3

81 = 3^{4}

Step

2

: Simplify the required term.

{(81)}^{\frac{3}{4}}

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

Using the exponents' law

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

can be written as

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

. Thus,

{(81)}^{\frac{3}{4}}

= 3^{3}

{(81)}^{\frac{3}{4}} = 27

.
Hence,

{(81)}^{\frac{3}{4}}

can be simplified as

27

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