Solve h^5216-39304

Question

Simplify the expression

216 h^{5} - 39304

Evaluate

h^{5} \times 216 - 39304

Solution

216 h^{5} - 39304

Show Solution

8 (27 h^{5} - 4913)

Evaluate

h^{5} \times 216 - 39304

Use the commutative property to reorder the terms

216 h^{5} - 39304

Solution

8 (27 h^{5} - 4913)

Show Solution

h = \frac{5 44217}{3}

Alternative Form

h \approx 2.83137

Evaluate

h^{5} \times 216 - 39304

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

h^{5} \times 216 - 39304 = 0

Use the commutative property to reorder the terms

216 h^{5} - 39304 = 0

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

216 h^{5} = 0 + 39304

Removing 0 doesn't change the value,so remove it from the expression

216 h^{5} = 39304

Divide both sides

\frac{216 h ^{5}}{216} = \frac{39304}{216}

Divide the numbers

h^{5} = \frac{39304}{216}

Cancel out the common factor 8

h^{5} = \frac{4913}{27}

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

5 h^{5} = 5 \frac{4913}{27}

Calculate

h = 5 \frac{4913}{27}

Solution

More Steps

Evaluate

5 \frac{4913}{27}

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

\frac{5 4913}{5 27}

Multiply by the Conjugate

\frac{5 4913 \times 5 2 7 ^{4}}{5 27 \times 5 2 7 ^{4}}

Simplify

\frac{5 4913 \times 3 ^{2} 5 9}{5 27 \times 5 2 7 ^{4}}

Multiply the numbers

More Steps

Evaluate

54913 \times 3^{2} 59

Multiply the terms

544217 \times 3^{2}

Use the commutative property to reorder the terms

3^{2} 544217

\frac{3 ^{2} 5 44217}{5 27 \times 5 2 7 ^{4}}

Multiply the numbers

More Steps

Evaluate

527 \times 5 2 7^{4}

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

5 27 \times 2 7^{4}

Calculate the product

5 2 7^{5}

Transform the expression

5 3^{15}

Reduce the index of the radical and exponent with 5

3^{3}

\frac{3 ^{2} 5 44217}{3 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{3 ^{2}}{3 ^{3}}

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

\frac{1}{3 ^{3 - 2}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{5 44217}{3}

h = \frac{5 44217}{3}

Alternative Form

h \approx 2.83137

Show Solution