Solve p^65p-e - ScanMath

Question

Simplify the expression

5 p^{7} - e

Evaluate

p^{6} \times 5 p - e

Solution

More Steps

Evaluate

p^{6} \times 5 p

Multiply the terms with the same base by adding their exponents

p^{6 + 1} \times 5

Add the numbers

p^{7} \times 5

Use the commutative property to reorder the terms

5 p^{7}

5 p^{7} - e

Show Solution

p = \frac{7 15625 e}{5}

Alternative Form

p \approx 0.91662

Evaluate

p^{6} \times 5 p - e

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

p^{6} \times 5 p - e = 0

Multiply

More Steps

Multiply the terms

p^{6} \times 5 p

Multiply the terms with the same base by adding their exponents

p^{6 + 1} \times 5

Add the numbers

p^{7} \times 5

Use the commutative property to reorder the terms

5 p^{7}

5 p^{7} - e = 0

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

5 p^{7} = 0 + e

Add the terms

5 p^{7} = e

Divide both sides

\frac{5 p ^{7}}{5} = \frac{e}{5}

Divide the numbers

p^{7} = \frac{e}{5}

Take the 7 -th root on both sides of the equation

7 p^{7} = 7 \frac{e}{5}

Calculate

p = 7 \frac{e}{5}

Solution

More Steps

Evaluate

7 \frac{e}{5}

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

\frac{7 e}{7 5}

Multiply by the Conjugate

\frac{7 e \times 7 5 ^{6}}{7 5 \times 7 5 ^{6}}

Simplify

\frac{7 e \times 7 15625}{7 5 \times 7 5 ^{6}}

Multiply the numbers

More Steps

Evaluate

7 e \times 715625

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

7 e \times 15625

Calculate the product

7 15625 e

\frac{7 15625 e}{7 5 \times 7 5 ^{6}}

Multiply the numbers

More Steps

Evaluate

75 \times 7 5^{6}

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

7 5 \times 5^{6}

Calculate the product

7 5^{7}

Reduce the index of the radical and exponent with 7

5

\frac{7 15625 e}{5}

p = \frac{7 15625 e}{5}

Alternative Form

p \approx 0.91662

Show Solution