Solve 64=9t^3t 16

Question

Solve the equation

t_{1} = - \frac{6}{3}, t_{2} = \frac{6}{3}

Alternative Form

t_{1} \approx - 0.816497, t_{2} \approx 0.816497

Evaluate

64 = 9 t^{3} \times t \times 16

Multiply

More Steps

Evaluate

9 t^{3} \times t \times 16

Multiply the terms

144 t^{3} \times t

Multiply the terms with the same base by adding their exponents

144 t^{3 + 1}

Add the numbers

144 t^{4}

64 = 144 t^{4}

Swap the sides of the equation

144 t^{4} = 64

Divide both sides

\frac{144 t ^{4}}{144} = \frac{64}{144}

Divide the numbers

t^{4} = \frac{64}{144}

Cancel out the common factor 16

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

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

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

Simplify the expression

More Steps

Evaluate

4 \frac{4}{9}

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

\frac{4 4}{4 9}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{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{2}{3}

Multiply by the Conjugate

\frac{2 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

2 \times 3

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

2 \times 3

Calculate the product

6

\frac{6}{3 \times 3}

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

\frac{6}{3}

t = \pm \frac{6}{3}

Separate the equation into 2 possible cases

t = \frac{6}{3} t = - \frac{6}{3}

Solution

t_{1} = - \frac{6}{3}, t_{2} = \frac{6}{3}

Alternative Form

t_{1} \approx - 0.816497, t_{2} \approx 0.816497

Show Solution