Solve 10p^24p 77=9

Question

Solve the equation

p = \frac{3 115 5 ^{2}}{770}

Alternative Form

p \approx 0.142965

Evaluate

10 p^{2} \times 4 p \times 77 = 9

Multiply

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Evaluate

10 p^{2} \times 4 p \times 77

Multiply the terms

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Evaluate

10 \times 4 \times 77

Multiply the terms

40 \times 77

Multiply the numbers

3080

3080 p^{2} \times p

Multiply the terms with the same base by adding their exponents

3080 p^{2 + 1}

Add the numbers

3080 p^{3}

3080 p^{3} = 9

Divide both sides

\frac{3080 p ^{3}}{3080} = \frac{9}{3080}

Divide the numbers

p^{3} = \frac{9}{3080}

Take the 3 -th root on both sides of the equation

3 p^{3} = 3 \frac{9}{3080}

Calculate

p = 3 \frac{9}{3080}

Solution

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Evaluate

3 \frac{9}{3080}

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

\frac{3 9}{3 3080}

Simplify the radical expression

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Evaluate

33080

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 385

Write the number in exponential form with the base of 2

3 2^{3} \times 385

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 3385

Reduce the index of the radical and exponent with 3

23385

\frac{3 9}{2 3 385}

Multiply by the Conjugate

\frac{3 9 \times 3 38 5 ^{2}}{2 3 385 \times 3 38 5 ^{2}}

Multiply the numbers

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Evaluate

39 \times 3 38 5^{2}

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

3 9 \times 38 5^{2}

Calculate the product

3 115 5^{2}

\frac{3 115 5 ^{2}}{2 3 385 \times 3 38 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

23385 \times 3 38 5^{2}

Multiply the terms

2 \times 385

Multiply the terms

770

\frac{3 115 5 ^{2}}{770}

p = \frac{3 115 5 ^{2}}{770}

Alternative Form

p \approx 0.142965

Show Solution