Solve 69x^6969x16 - 161

Question

Simplify the expression

1069776 x^{7} - 161

Evaluate

69 x^{6} \times 969 x \times 16 - 161

Solution

More Steps

Evaluate

69 x^{6} \times 969 x \times 16

Multiply the terms

More Steps

Evaluate

69 \times 969 \times 16

Multiply the terms

66861 \times 16

Multiply the numbers

1069776

1069776 x^{6} \times x

Multiply the terms with the same base by adding their exponents

1069776 x^{6 + 1}

Add the numbers

1069776 x^{7}

1069776 x^{7} - 161

Show Solution

Factor the expression

23 (46512 x^{7} - 7)

Evaluate

69 x^{6} \times 969 x \times 16 - 161

Multiply

More Steps

Evaluate

69 x^{6} \times 969 x \times 16

Multiply the terms

More Steps

Evaluate

69 \times 969 \times 16

Multiply the terms

66861 \times 16

Multiply the numbers

1069776

1069776 x^{6} \times x

Multiply the terms with the same base by adding their exponents

1069776 x^{6 + 1}

Add the numbers

1069776 x^{7}

1069776 x^{7} - 161

Solution

23 (46512 x^{7} - 7)

Show Solution

Find the roots

x = \frac{7 7 \times 4651 2 ^{6}}{46512}

Alternative Form

x \approx 0.284402

Evaluate

69 x^{6} \times 969 x \times 16 - 161

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

69 x^{6} \times 969 x \times 16 - 161 = 0

Multiply

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Multiply the terms

69 x^{6} \times 969 x \times 16

Multiply the terms

More Steps

Evaluate

69 \times 969 \times 16

Multiply the terms

66861 \times 16

Multiply the numbers

1069776

1069776 x^{6} \times x

Multiply the terms with the same base by adding their exponents

1069776 x^{6 + 1}

Add the numbers

1069776 x^{7}

1069776 x^{7} - 161 = 0

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

1069776 x^{7} = 0 + 161

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

1069776 x^{7} = 161

Divide both sides

\frac{1069776 x ^{7}}{1069776} = \frac{161}{1069776}

Divide the numbers

x^{7} = \frac{161}{1069776}

Cancel out the common factor 23

x^{7} = \frac{7}{46512}

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

7 x^{7} = 7 \frac{7}{46512}

Calculate

x = 7 \frac{7}{46512}

Solution

More Steps

Evaluate

7 \frac{7}{46512}

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

\frac{7 7}{7 46512}

Multiply by the Conjugate

\frac{7 7 \times 7 4651 2 ^{6}}{7 46512 \times 7 4651 2 ^{6}}

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

\frac{7 7 \times 4651 2 ^{6}}{7 46512 \times 7 4651 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

746512 \times 7 4651 2^{6}

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

7 46512 \times 4651 2^{6}

Calculate the product

7 4651 2^{7}

Reduce the index of the radical and exponent with 7

46512

\frac{7 7 \times 4651 2 ^{6}}{46512}

x = \frac{7 7 \times 4651 2 ^{6}}{46512}

Alternative Form

x \approx 0.284402

Show Solution