Solve (3x^3 4x^4-5)/ sqrt(3^2 4^2)

Question

Simplify the expression

\frac{12 x ^{7} - 5}{12}

Evaluate

\frac{3 x ^{3} \times 4 x ^{4} - 5}{3 ^{2} \times 4 ^{2}}

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{3 + 4}

Add the numbers

12 x^{7}

\frac{12 x ^{7} - 5}{3 ^{2} \times 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

3^{2} \times 4^{2}

Multiply the terms with equal exponents by multiplying their bases

(3 \times 4)^{2}

Multiply the numbers

1 2^{2}

\frac{12 x ^{7} - 5}{1 2 ^{2}}

Solution

\frac{12 x ^{7} - 5}{12}

Show Solution

Find the roots

x = \frac{7 5 \times 1 2 ^{6}}{12}

Alternative Form

x \approx 0.882438

Evaluate

\frac{3 x ^{3} \times 4 x ^{4} - 5}{3 ^{2} \times 4 ^{2}}

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

\frac{3 x ^{3} \times 4 x ^{4} - 5}{3 ^{2} \times 4 ^{2}} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{3 + 4}

Add the numbers

12 x^{7}

\frac{12 x ^{7} - 5}{3 ^{2} \times 4 ^{2}} = 0

Multiply the numbers

More Steps

Evaluate

3^{2} \times 4^{2}

Multiply the terms with equal exponents by multiplying their bases

(3 \times 4)^{2}

Multiply the numbers

1 2^{2}

\frac{12 x ^{7} - 5}{1 2 ^{2}} = 0

Reduce the index of the radical and exponent with 2

\frac{12 x ^{7} - 5}{12} = 0

Simplify

12 x^{7} - 5 = 0

Move the constant to the right side

12 x^{7} = 5

Divide both sides

\frac{12 x ^{7}}{12} = \frac{5}{12}

Divide the numbers

x^{7} = \frac{5}{12}

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

7 x^{7} = 7 \frac{5}{12}

Calculate

x = 7 \frac{5}{12}

Solution

More Steps

Evaluate

7 \frac{5}{12}

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

\frac{7 5}{7 12}

Multiply by the Conjugate

\frac{7 5 \times 7 1 2 ^{6}}{7 12 \times 7 1 2 ^{6}}

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

\frac{7 5 \times 1 2 ^{6}}{7 12 \times 7 1 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

712 \times 7 1 2^{6}

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

7 12 \times 1 2^{6}

Calculate the product

7 1 2^{7}

Reduce the index of the radical and exponent with 7

12

\frac{7 5 \times 1 2 ^{6}}{12}

x = \frac{7 5 \times 1 2 ^{6}}{12}

Alternative Form

x \approx 0.882438

Show Solution