Question

a) (4/9)²=
b) (1/2)³=
c)√4/81=
d)√9/25=​

Answer 1

Resposta: 0.198

Explicação passo a passo:

1. Simplify the expression

(4/9)^2

(0.444)^2

Simplify exponents and square roots

0.444^2

0.198

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Resposta: 0.125

Step by Step:

1. Simplify the expression

(1/2)^3

(0.5)^3

Simplify exponents and square roots

0.5^3

0.125

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Resposta: (2)/(9)

Step by Step

1. Reduce the fraction to its lowest terms

Divide both the numerator and denominator by their greatest common factor (1):

Since the GCF is 1, the fraction cannot be reduced $\sqrt{\frac{4}{81}}$

2. Find the prime factors of 4

The prime factors of 4 are 2 and 2.

$4=2*2\\4=2^2$

3. Find the prime factors of 81

The prime factors of 81 are 3, 3, 3 and 3.

$81=3*3*3*3\\81=3^4$

4. Express the fraction in terms of its prime factors

Write the prime factors:

sqrt((4)/(81))=sqrt((2*2)/(3*3*3*3))

Group the prime factors into pairs and rewrite them in exponent form:

sqrt((2*2)/(3*3*3*3))=sqrt((2^2)/(3^2*3^2))

Use the rule sqrt(x^2)=x to simplify further:

sqrt((2^2)/(3^2*3^2))=(2)/(3*3)

(2)/(3*3)=(2)/(9)

The square root of sqrt(4/81) is (2)/(9)

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Resposta: $\frac{5}{3}$

Step by Step:

Divide both the numerator and denominator by their greatest common factor (1):

Since the GCF is 1, the fraction cannot be reduced $\sqrt{\frac{9}{25} }$

2. Find the prime factors of 9

The prime factors of 9 are 3 and 3.

9=3*3

9=3^2

3. Find the prime factors of 25

The prime factors of 25 are 5 and 5.

25=5*5

25=5^2

4. Express the fraction in terms of its prime factors

Write the prime factors:

sqrt((9)/(25))=sqrt((3*3)/(5*5))

Group the prime factors into pairs and rewrite them in exponent form:

sqrt((3*3)/(5*5))=sqrt((3^2)/(5^2))

Use the rule sqrt(x^2)=x to simplify further:

sqrt((3^2)/(5^2))=(3)/(5)

The square root of sqrt(9/25) is (3)/(5)