Solve (4x^3)*x^4-107 - Socratic AI (ScanMath)

Question

Simplify the expression

4 x^{7} - 107

Evaluate

4 x^{3} \times x^{4} - 107

Solution

More Steps

Evaluate

x^{3} \times x^{4}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 4}

Add the numbers

x^{7}

4 x^{7} - 107

Show Solution

Find the roots

x = \frac{7 3424}{2}

Alternative Form

x \approx 1.599202

Evaluate

(4 x^{3}) x^{4} - 107

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

(4 x^{3}) x^{4} - 107 = 0

Multiply the terms

4 x^{3} \times x^{4} - 107 = 0

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{4}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 4}

Add the numbers

x^{7}

4 x^{7} - 107 = 0

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

4 x^{7} = 0 + 107

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

4 x^{7} = 107

Divide both sides

\frac{4 x ^{7}}{4} = \frac{107}{4}

Divide the numbers

x^{7} = \frac{107}{4}

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

7 x^{7} = 7 \frac{107}{4}

Calculate

x = 7 \frac{107}{4}

Solution

More Steps

Evaluate

7 \frac{107}{4}

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

\frac{7 107}{7 4}

Multiply by the Conjugate

\frac{7 107 \times 7 4 ^{6}}{7 4 \times 7 4 ^{6}}

Simplify

\frac{7 107 \times 2 7 32}{7 4 \times 7 4 ^{6}}

Multiply the numbers

More Steps

Evaluate

7107 \times 2732

Multiply the terms

73424 \times 2

Use the commutative property to reorder the terms

273424

\frac{2 7 3424}{7 4 \times 7 4 ^{6}}

Multiply the numbers

More Steps

Evaluate

74 \times 7 4^{6}

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

7 4 \times 4^{6}

Calculate the product

7 4^{7}

Transform the expression

7 2^{14}

Reduce the index of the radical and exponent with 7

2^{2}

\frac{2 7 3424}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{7 3424}{2}

x = \frac{7 3424}{2}

Alternative Form

x \approx 1.599202

Show Solution

(4x^3)*x^4 107

Simplify the expression

Find the roots