Question

simplify : 3 ^30+3^29+3^28/3^31+3^30-3^29​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of $\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$ is $\frac{13}{33}$.

Step-by-step explanation:

Given:

$\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$

To Find:

The value of $\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$.

Concept Used:

An exponent is referred to a number or a variable raised to another number or variable. An exponential number can be written as an, where p= base and q = exponent. The laws of exponents are  for different types of operations performed on exponents such as addition, multiplication and division.

It is denoted as,$p^{q}$ , here, q is known as the exponent of p.

Solution:

As given,$\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$.

$\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$

$=\frac{3^{28} (3^{2}+3^{1} +1)}{3^{29} (3^{2}+3^{1} -1)}$

$=\frac{ (9+3+1)}{3^{(29-30)}\times (9+3 -1)}$

$=\frac{13}{3\times11}$

$=\frac{13}{33}$

Thus,the value of $\frac{3^{30}+3^{29} +3^{28} }{3^{31}+3^{30} -3^{29} }$ is $\frac{13}{33}$.

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Answer 3

Answer: $\frac{3^{30}\ +\ 3^{29}\ +\ 3^{28}}{3^{31}\ +\ 3^{30}\ -\ 3^{29}}$ = 13/33

Step-by-step explanation:

given, $\frac{3^{30}\ +\ 3^{29}\ +\ 3^{28}}{3^{31}\ +\ 3^{30}\ -\ 3^{29}}$ to simplify

here, the numerator is 3³⁰ + 3²⁹ + 3²⁸

it can be simplified by taking the 3²⁸ as a common factor

therefore, the numerator will be simplified as

⇒ 3³⁰ + 3²⁸ + 3²⁸ = 3 × 3 × 3²⁸ + 3 × 3²⁸ + 3²⁸

                            = 3³⁰ + 3²⁸ ( 3 + 1 ) = 3 × 3 × 3²⁸ + 3²⁸ × 4

                            = 3²⁸ ( 9 + 4 )

                            = 13 × 3²⁸

Therefore, the numerator is 13 × 3²⁸

similarly, the given denominator is 3³¹ + 3³⁰ - 3²⁹

it can be simplified by taking the 3²⁹ as a common factor

Therefore, the denominator will be simplified as

⇒ 3³¹+3³⁰-3²⁹ = 3 × 3 × 3²⁹ + 3 × 3²⁹ - 3²⁹ = 3³¹ +  3²⁹ ( 3 - 1 )

                      = 3 × 3 × 3²⁹ + 2 × 3²⁹

                      = 3²⁹ ( 9 + 2 )

                      = 11 × 3²⁹

Therefore, the denominator is 11 × 3²⁹

Now, to simplify

(numerator/denominator) = 13 × 3²⁸ / 11 × 3²⁹

                                          = 13 / (11 × 3)

                                          = 13 / 33

Therefore, after the simplification, we get 13/33

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