Solve p= 3x^3x^3x1

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{7 729 x}{3}

Evaluate

p = 3 x^{3} \times x^{3} \times x \times 1

Simplify

More Steps

Evaluate

3 x^{3} \times x^{3} \times x \times 1

Rewrite the expression

3 x^{3} \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

3 x^{3 + 3 + 1}

Add the numbers

3 x^{7}

p = 3 x^{7}

Interchange x and y

x = 3 y^{7}

Swap the sides of the equation

3 y^{7} = x

Divide both sides

\frac{3 y ^{7}}{3} = \frac{x}{3}

Divide the numbers

y^{7} = \frac{x}{3}

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

7 y^{7} = 7 \frac{x}{3}

Calculate

y = 7 \frac{x}{3}

Simplify the root

More Steps

Evaluate

7 \frac{x}{3}

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

\frac{7 x}{7 3}

Multiply by the Conjugate

\frac{7 x \times 7 3 ^{6}}{7 3 \times 7 3 ^{6}}

Calculate

\frac{7 x \times 7 3 ^{6}}{3}

Calculate

More Steps

Evaluate

7 x \times 7 3^{6}

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

7 x \times 3^{6}

Calculate the product

7 3^{6} x

\frac{7 3 ^{6} x}{3}

Calculate

\frac{7 729 x}{3}

y = \frac{7 729 x}{3}

Solution

f^{- 1} (x) = \frac{7 729 x}{3}

Show Solution

Solve the equation

Solve for x

Solve for p

x = \frac{7 729 p}{3}

Evaluate

p = 3 x^{3} \times x^{3} \times x \times 1

Simplify

More Steps

Evaluate

3 x^{3} \times x^{3} \times x \times 1

Rewrite the expression

3 x^{3} \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

3 x^{3 + 3 + 1}

Add the numbers

3 x^{7}

p = 3 x^{7}

Swap the sides of the equation

3 x^{7} = p

Divide both sides

\frac{3 x ^{7}}{3} = \frac{p}{3}

Divide the numbers

x^{7} = \frac{p}{3}

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

7 x^{7} = 7 \frac{p}{3}

Calculate

x = 7 \frac{p}{3}

Solution

More Steps

Evaluate

7 \frac{p}{3}

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

\frac{7 p}{7 3}

Multiply by the Conjugate

\frac{7 p \times 7 3 ^{6}}{7 3 \times 7 3 ^{6}}

Calculate

\frac{7 p \times 7 3 ^{6}}{3}

Calculate

More Steps

Evaluate

7 p \times 7 3^{6}

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

7 p \times 3^{6}

Calculate the product

7 3^{6} p

\frac{7 3 ^{6} p}{3}

Calculate

\frac{7 729 p}{3}

x = \frac{7 729 p}{3}

Show Solution

Function

Solve the equation

Graph