Solve t*t^39 = 13

Question

Solve the equation

t_{1} = - \frac{4 117}{3}, t_{2} = \frac{4 117}{3}

Alternative Form

t_{1} \approx - 1.096289, t_{2} \approx 1.096289

Evaluate

t \times t^{3} \times 9 = 13

Multiply

More Steps

Evaluate

t \times t^{3} \times 9

Multiply the terms with the same base by adding their exponents

t^{1 + 3} \times 9

Add the numbers

t^{4} \times 9

Use the commutative property to reorder the terms

9 t^{4}

9 t^{4} = 13

Divide both sides

\frac{9 t ^{4}}{9} = \frac{13}{9}

Divide the numbers

t^{4} = \frac{13}{9}

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

t = \pm 4 \frac{13}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{13}{9}

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

\frac{4 13}{4 9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4 13}{3}

Multiply by the Conjugate

\frac{4 13 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

413 \times 3

Use n a = mn a^{m} to expand the expression

413 \times 4 3^{2}

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

4 13 \times 3^{2}

Calculate the product

4117

\frac{4 117}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 117}{3}

t = \pm \frac{4 117}{3}

Separate the equation into 2 possible cases

t = \frac{4 117}{3} t = - \frac{4 117}{3}

Solution

t_{1} = - \frac{4 117}{3}, t_{2} = \frac{4 117}{3}

Alternative Form

t_{1} \approx - 1.096289, t_{2} \approx 1.096289

Show Solution