Solve 512=5x^47 - ScanMath

Question

Solve the equation

x_{1} = - \frac{4 4 85750}{35}, x_{2} = \frac{4 4 85750}{35}

Alternative Form

x_{1} \approx - 1.955692, x_{2} \approx 1.955692

Evaluate

512 = 5 x^{4} \times 7

Multiply the terms

512 = 35 x^{4}

Swap the sides of the equation

35 x^{4} = 512

Divide both sides

\frac{35 x ^{4}}{35} = \frac{512}{35}

Divide the numbers

x^{4} = \frac{512}{35}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{512}{35}

Simplify the expression

More Steps

Evaluate

4 \frac{512}{35}

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

\frac{4 512}{4 35}

Simplify the radical expression

More Steps

Evaluate

4512

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

4 256 \times 2

Write the number in exponential form with the base of 4

4 4^{4} \times 2

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

4 4^{4} \times 42

Reduce the index of the radical and exponent with 4

442

\frac{4 4 2}{4 35}

Multiply by the Conjugate

\frac{4 4 2 \times 4 3 5 ^{3}}{4 35 \times 4 3 5 ^{3}}

Simplify

\frac{4 4 2 \times 4 42875}{4 35 \times 4 3 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 442875

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

4 2 \times 42875

Calculate the product

485750

\frac{4 4 85750}{4 35 \times 4 3 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

435 \times 4 3 5^{3}

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

4 35 \times 3 5^{3}

Calculate the product

4 3 5^{4}

Reduce the index of the radical and exponent with 4

35

\frac{4 4 85750}{35}

x = \pm \frac{4 4 85750}{35}

Separate the equation into 2 possible cases

x = \frac{4 4 85750}{35} x = - \frac{4 4 85750}{35}

Solution

x_{1} = - \frac{4 4 85750}{35}, x_{2} = \frac{4 4 85750}{35}

Alternative Form

x_{1} \approx - 1.955692, x_{2} \approx 1.955692

Show Solution