Solve 56-3a^651 - ScanMath

Question

Simplify the expression

56 - 153 a^{6}

Evaluate

56 - 3 a^{6} \times 51

Solution

56 - 153 a^{6}

Show Solution

a_{1} = - \frac{6 56 \times 15 3 ^{5}}{153}, a_{2} = \frac{6 56 \times 15 3 ^{5}}{153}

Alternative Form

a_{1} \approx - 0.845764, a_{2} \approx 0.845764

Evaluate

56 - 3 a^{6} \times 51

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

56 - 3 a^{6} \times 51 = 0

Multiply the terms

56 - 153 a^{6} = 0

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

- 153 a^{6} = 0 - 56

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

- 153 a^{6} = - 56

Change the signs on both sides of the equation

153 a^{6} = 56

Divide both sides

\frac{153 a ^{6}}{153} = \frac{56}{153}

Divide the numbers

a^{6} = \frac{56}{153}

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

a = \pm 6 \frac{56}{153}

Simplify the expression

More Steps

Evaluate

6 \frac{56}{153}

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

\frac{6 56}{6 153}

Multiply by the Conjugate

\frac{6 56 \times 6 15 3 ^{5}}{6 153 \times 6 15 3 ^{5}}

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

\frac{6 56 \times 15 3 ^{5}}{6 153 \times 6 15 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

6153 \times 6 15 3^{5}

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

6 153 \times 15 3^{5}

Calculate the product

6 15 3^{6}

Reduce the index of the radical and exponent with 6

153

\frac{6 56 \times 15 3 ^{5}}{153}

a = \pm \frac{6 56 \times 15 3 ^{5}}{153}

Separate the equation into 2 possible cases

a = \frac{6 56 \times 15 3 ^{5}}{153} a = - \frac{6 56 \times 15 3 ^{5}}{153}

Solution

a_{1} = - \frac{6 56 \times 15 3 ^{5}}{153}, a_{2} = \frac{6 56 \times 15 3 ^{5}}{153}

Alternative Form

a_{1} \approx - 0.845764, a_{2} \approx 0.845764

Show Solution