Solve -7u^24(-u^27) -7 - Socratic AI (ScanMath)

Question

Simplify the expression

196 u^{4} - 7

Evaluate

- 7 u^{2} \times 4 (- u^{2} \times 7) - 7

Use the commutative property to reorder the terms

- 7 u^{2} \times 4 (- 7 u^{2}) - 7

Solution

More Steps

Multiply the terms

- 7 u^{2} \times 4 (- 7 u^{2})

Rewrite the expression

7 u^{2} \times 4 \times 7 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 4 \times 7

Multiply the terms

28 \times 7

Multiply the numbers

196

196 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

196 u^{2 + 2}

Add the numbers

196 u^{4}

196 u^{4} - 7

Show Solution

Factor the expression

7 (28 u^{4} - 1)

Evaluate

- 7 u^{2} \times 4 (- u^{2} \times 7) - 7

Use the commutative property to reorder the terms

- 7 u^{2} \times 4 (- 7 u^{2}) - 7

Multiply

More Steps

Multiply the terms

- 7 u^{2} \times 4 (- 7 u^{2})

Rewrite the expression

7 u^{2} \times 4 \times 7 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 4 \times 7

Multiply the terms

28 \times 7

Multiply the numbers

196

196 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

196 u^{2 + 2}

Add the numbers

196 u^{4}

196 u^{4} - 7

Solution

7 (28 u^{4} - 1)

Show Solution

Find the roots

u_{1} = - \frac{4 1372}{14}, u_{2} = \frac{4 1372}{14}

Alternative Form

u_{1} \approx - 0.434721, u_{2} \approx 0.434721

Evaluate

- 7 u^{2} \times 4 (- u^{2} \times 7) - 7

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

- 7 u^{2} \times 4 (- u^{2} \times 7) - 7 = 0

Use the commutative property to reorder the terms

- 7 u^{2} \times 4 (- 7 u^{2}) - 7 = 0

Multiply

More Steps

Multiply the terms

- 7 u^{2} \times 4 (- 7 u^{2})

Rewrite the expression

7 u^{2} \times 4 \times 7 u^{2}

Multiply the terms

More Steps

Evaluate

7 \times 4 \times 7

Multiply the terms

28 \times 7

Multiply the numbers

196

196 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

196 u^{2 + 2}

Add the numbers

196 u^{4}

196 u^{4} - 7 = 0

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

196 u^{4} = 0 + 7

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

196 u^{4} = 7

Divide both sides

\frac{196 u ^{4}}{196} = \frac{7}{196}

Divide the numbers

u^{4} = \frac{7}{196}

Cancel out the common factor 7

u^{4} = \frac{1}{28}

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

u = \pm 4 \frac{1}{28}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{28}

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

\frac{4 1}{4 28}

Simplify the radical expression

\frac{1}{4 28}

Multiply by the Conjugate

\frac{4 2 8 ^{3}}{4 28 \times 4 2 8 ^{3}}

Simplify

\frac{2 4 1372}{4 28 \times 4 2 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

428 \times 4 2 8^{3}

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

4 28 \times 2 8^{3}

Calculate the product

4 2 8^{4}

Reduce the index of the radical and exponent with 4

28

\frac{2 4 1372}{28}

Cancel out the common factor 2

\frac{4 1372}{14}

u = \pm \frac{4 1372}{14}

Separate the equation into 2 possible cases

u = \frac{4 1372}{14} u = - \frac{4 1372}{14}

Solution

u_{1} = - \frac{4 1372}{14}, u_{2} = \frac{4 1372}{14}

Alternative Form

u_{1} \approx - 0.434721, u_{2} \approx 0.434721

Show Solution

7u^24( U^27) 7

Simplify the expression

Factor the expression

Find the roots