Solve 1g^643-33000

Question

Simplify the expression

43 g^{6} - 33000

Evaluate

1 \times g^{6} \times 43 - 33000

Solution

More Steps

Evaluate

1 \times g^{6} \times 43

Rewrite the expression

g^{6} \times 43

Use the commutative property to reorder the terms

43 g^{6}

43 g^{6} - 33000

Show Solution

g_{1} = - \frac{6 33000 \times 4 3 ^{5}}{43}, g_{2} = \frac{6 33000 \times 4 3 ^{5}}{43}

Alternative Form

g_{1} \approx - 3.025805, g_{2} \approx 3.025805

Evaluate

1 \times g^{6} \times 43 - 33000

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

1 \times g^{6} \times 43 - 33000 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times g^{6} \times 43

Rewrite the expression

g^{6} \times 43

Use the commutative property to reorder the terms

43 g^{6}

43 g^{6} - 33000 = 0

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

43 g^{6} = 0 + 33000

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

43 g^{6} = 33000

Divide both sides

\frac{43 g ^{6}}{43} = \frac{33000}{43}

Divide the numbers

g^{6} = \frac{33000}{43}

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

g = \pm 6 \frac{33000}{43}

Simplify the expression

More Steps

Evaluate

6 \frac{33000}{43}

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

\frac{6 33000}{6 43}

Multiply by the Conjugate

\frac{6 33000 \times 6 4 3 ^{5}}{6 43 \times 6 4 3 ^{5}}

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

\frac{6 33000 \times 4 3 ^{5}}{6 43 \times 6 4 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

643 \times 6 4 3^{5}

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

6 43 \times 4 3^{5}

Calculate the product

6 4 3^{6}

Reduce the index of the radical and exponent with 6

43

\frac{6 33000 \times 4 3 ^{5}}{43}

g = \pm \frac{6 33000 \times 4 3 ^{5}}{43}

Separate the equation into 2 possible cases

g = \frac{6 33000 \times 4 3 ^{5}}{43} g = - \frac{6 33000 \times 4 3 ^{5}}{43}

Solution

g_{1} = - \frac{6 33000 \times 4 3 ^{5}}{43}, g_{2} = \frac{6 33000 \times 4 3 ^{5}}{43}

Alternative Form

g_{1} \approx - 3.025805, g_{2} \approx 3.025805

Show Solution