Solve r^414-16 - ScanMath

Question

Simplify the expression

14 r^{4} - 16

Evaluate

r^{4} \times 14 - 16

Solution

14 r^{4} - 16

Show Solution

2 (7 r^{4} - 8)

Evaluate

r^{4} \times 14 - 16

Use the commutative property to reorder the terms

14 r^{4} - 16

Solution

2 (7 r^{4} - 8)

Show Solution

r_{1} = - \frac{4 2744}{7}, r_{2} = \frac{4 2744}{7}

Alternative Form

r_{1} \approx - 1.033946, r_{2} \approx 1.033946

Evaluate

r^{4} \times 14 - 16

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

r^{4} \times 14 - 16 = 0

Use the commutative property to reorder the terms

14 r^{4} - 16 = 0

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

14 r^{4} = 0 + 16

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

14 r^{4} = 16

Divide both sides

\frac{14 r ^{4}}{14} = \frac{16}{14}

Divide the numbers

r^{4} = \frac{16}{14}

Cancel out the common factor 2

r^{4} = \frac{8}{7}

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

r = \pm 4 \frac{8}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{8}{7}

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

\frac{4 8}{4 7}

Multiply by the Conjugate

\frac{4 8 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 8 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4343

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

4 8 \times 343

Calculate the product

42744

\frac{4 2744}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 2744}{7}

r = \pm \frac{4 2744}{7}

Separate the equation into 2 possible cases

r = \frac{4 2744}{7} r = - \frac{4 2744}{7}

Solution

r_{1} = - \frac{4 2744}{7}, r_{2} = \frac{4 2744}{7}

Alternative Form

r_{1} \approx - 1.033946, r_{2} \approx 1.033946

Show Solution