Solve 6^2x^2*6^3x=1

Question

Solve the equation

x = \frac{3 6}{36}

Alternative Form

x \approx 0.050476

Evaluate

6^{2} x^{2} \times 6^{3} x = 1

Multiply

More Steps

Evaluate

6^{2} x^{2} \times 6^{3} x

Multiply the terms with the same base by adding their exponents

6^{2 + 3} x^{2} \times x

Add the numbers

6^{5} x^{2} \times x

Multiply the terms with the same base by adding their exponents

6^{5} x^{2 + 1}

Add the numbers

6^{5} x^{3}

6^{5} x^{3} = 1

Divide both sides

\frac{6 ^{5} x ^{3}}{6 ^{5}} = \frac{1}{6 ^{5}}

Divide the numbers

x^{3} = \frac{1}{6 ^{5}}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{6 ^{5}}

Calculate

x = 3 \frac{1}{6 ^{5}}

Simplify the root

More Steps

Evaluate

3 \frac{1}{6 ^{5}}

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

\frac{3 1}{3 6 ^{5}}

Simplify the radical expression

\frac{1}{3 6 ^{5}}

Simplify the radical expression

More Steps

Evaluate

3 6^{5}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

3 6^{3 + 2}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

3 6^{3} \times 6^{2}

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

3 6^{3} \times 3 6^{2}

Reduce the index of the radical and exponent with 3

6 3 6^{2}

Simplify the radical expression

6336

\frac{1}{6 3 36}

Multiply by the Conjugate

\frac{3 3 6 ^{2}}{6 3 36 \times 3 3 6 ^{2}}

Simplify

\frac{6 3 6}{6 3 36 \times 3 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

6336 \times 3 3 6^{2}

Multiply the terms

6 \times 6^{2}

Calculate the product

6^{3}

\frac{6 3 6}{6 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{6}{6 ^{3}}

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

\frac{1}{6 ^{3 - 1}}

Subtract the terms

\frac{1}{6 ^{2}}

\frac{3 6}{6 ^{2}}

x = \frac{3 6}{6 ^{2}}

Solution

x = \frac{3 6}{36}

Alternative Form

x \approx 0.050476

Show Solution