Solve a^57-377/2023

Question

Simplify the expression

7 a^{5} - \frac{377}{2023}

Evaluate

a^{5} \times 7 - \frac{377}{2023}

Solution

7 a^{5} - \frac{377}{2023}

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Factor the expression

\frac{1}{2023} (14161 a^{5} - 377)

Evaluate

a^{5} \times 7 - \frac{377}{2023}

Use the commutative property to reorder the terms

7 a^{5} - \frac{377}{2023}

Solution

\frac{1}{2023} (14161 a^{5} - 377)

Show Solution

Find the roots

a = \frac{5 377 \times 11 9 ^{3}}{119}

Alternative Form

a \approx 0.484228

Evaluate

a^{5} \times 7 - \frac{377}{2023}

To find the roots of the expression,set the expression equal to 0

a^{5} \times 7 - \frac{377}{2023} = 0

Use the commutative property to reorder the terms

7 a^{5} - \frac{377}{2023} = 0

Move the constant to the right-hand side and change its sign

7 a^{5} = 0 + \frac{377}{2023}

Add the terms

7 a^{5} = \frac{377}{2023}

Multiply by the reciprocal

7 a^{5} \times \frac{1}{7} = \frac{377}{2023} \times \frac{1}{7}

Multiply

a^{5} = \frac{377}{2023} \times \frac{1}{7}

Multiply

More Steps

Evaluate

\frac{377}{2023} \times \frac{1}{7}

To multiply the fractions,multiply the numerators and denominators separately

\frac{377}{2023 \times 7}

Multiply the numbers

\frac{377}{14161}

a^{5} = \frac{377}{14161}

Take the 5 -th root on both sides of the equation

5 a^{5} = 5 \frac{377}{14161}

Calculate

a = 5 \frac{377}{14161}

Solution

More Steps

Evaluate

5 \frac{377}{14161}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5 377}{5 14161}

Multiply by the Conjugate

\frac{5 377 \times 5 1416 1 ^{4}}{5 14161 \times 5 1416 1 ^{4}}

Simplify

\frac{5 377 \times 119 5 11 9 ^{3}}{5 14161 \times 5 1416 1 ^{4}}

Multiply the numbers

More Steps

Evaluate

5377 \times 119 5 11 9^{3}

The product of roots with the same index is equal to the root of the product

5 377 \times 11 9^{3} \times 119

Use the commutative property to reorder the terms

119 5 377 \times 11 9^{3}

\frac{119 5 377 \times 11 9 ^{3}}{5 14161 \times 5 1416 1 ^{4}}

Multiply the numbers

More Steps

Evaluate

514161 \times 5 1416 1^{4}

The product of roots with the same index is equal to the root of the product

5 14161 \times 1416 1^{4}

Calculate the product

5 1416 1^{5}

Transform the expression

5 11 9^{10}

Reduce the index of the radical and exponent with 5

11 9^{2}

\frac{119 5 377 \times 11 9 ^{3}}{11 9 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{119}{11 9 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{11 9 ^{2 - 1}}

Subtract the terms

\frac{1}{11 9 ^{1}}

Simplify

\frac{1}{119}

\frac{5 377 \times 11 9 ^{3}}{119}

a = \frac{5 377 \times 11 9 ^{3}}{119}

Alternative Form

a \approx 0.484228

Show Solution