Solve 3^-5x10^-5x125/5^-7x^6^-5

Question

Simplify the expression

\frac{3125}{7776} x^{8} - 5

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\frac{5}{6 ^{5}} \times (625 x^{8} - 7776)

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x_{1} = - \frac{8 4860000}{5}, x_{2} = \frac{8 4860000}{5}

Alternative Form

x_{1} \approx - 1.370438, x_{2} \approx 1.370438

Evaluate

3^{- 5} x \times 1 0^{- 5} x \times \frac{125}{5 ^{- 7}} \times x^{6} - 5

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

3^{- 5} x \times 1 0^{- 5} x \times \frac{125}{5 ^{- 7}} \times x^{6} - 5 = 0

Divide the terms

More Steps

3^{- 5} x \times 1 0^{- 5} x \times 5^{10} x^{6} - 5 = 0

Multiply

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\frac{5 ^{5}}{6 ^{5}} \times x^{8} - 5 = 0

Evaluate the power

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\frac{3125}{7776} x^{8} - 5 = 0

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

\frac{3125}{7776} x^{8} = 0 + 5

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

\frac{3125}{7776} x^{8} = 5

Multiply by the reciprocal

\frac{3125}{7776} x^{8} \times \frac{7776}{3125} = 5 \times \frac{7776}{3125}

Multiply

x^{8} = 5 \times \frac{7776}{3125}

Multiply

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x^{8} = \frac{7776}{625}

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

x = \pm 8 \frac{7776}{625}

Simplify the expression

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x = \pm \frac{8 4860000}{5}

Separate the equation into 2 possible cases

x = \frac{8 4860000}{5} x = - \frac{8 4860000}{5}

Solution

x_{1} = - \frac{8 4860000}{5}, x_{2} = \frac{8 4860000}{5}

Alternative Form

x_{1} \approx - 1.370438, x_{2} \approx 1.370438

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