Solve (9n^(7)-1)^(2) - Socratic AI (ScanMath)

问题

Simplify the expression

81 n^{14} - 18 n^{7} + 1

Evaluate

(9 n^{7} - 1)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(9 n^{7})^{2} - 2 \times 9 n^{7} \times 1 + 1^{2}

解题方案

81 n^{14} - 18 n^{7} + 1

显示解题方案

n = \frac{7 243}{3}

Alternative Form

n \approx 0.7306

Evaluate

(9 n^{7} - 1)^{2}

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

(9 n^{7} - 1)^{2} = 0

The only way a power can be 0 is when the base equals 0

9 n^{7} - 1 = 0

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

9 n^{7} = 0 + 1

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

9 n^{7} = 1

Divide both sides

\frac{9 n ^{7}}{9} = \frac{1}{9}

Divide the numbers

n^{7} = \frac{1}{9}

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

7 n^{7} = 7 \frac{1}{9}

Calculate

n = 7 \frac{1}{9}

解题方案

更多步骤

Evaluate

7 \frac{1}{9}

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

\frac{7 1}{7 9}

Simplify the radical expression

\frac{1}{7 9}

Multiply by the Conjugate

\frac{7 9 ^{6}}{7 9 \times 7 9 ^{6}}

Simplify

\frac{3 7 243}{7 9 \times 7 9 ^{6}}

Multiply the numbers

更多步骤

Evaluate

79 \times 7 9^{6}

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

7 9 \times 9^{6}

Calculate the product

7 9^{7}

Transform the expression

7 3^{14}

Reduce the index of the radical and exponent with 7

3^{2}

\frac{3 7 243}{3 ^{2}}

Reduce the fraction

更多步骤

Evaluate

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

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

\frac{1}{3 ^{2 - 1}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{7 243}{3}

n = \frac{7 243}{3}

Alternative Form

n \approx 0.7306

显示解题方案