Solve frac{(m^{2}*m)^{3}divm^5}{m^6(m^2)^-4}

$$\frac { ( m ^ { 2 } \times m ) ^ { 3 } \div m ^ { 5 } } { m ^ { 6 } ( m ^ { 2 } ) ^ { - 4 } }$$

Evaluate

$$m^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\frac{\left(m^{3}\right)^{3}}{m^{5}}}{m^{6}\left(m^{2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{m^{9}}{m^{5}}}{m^{6}\left(m^{2}\right)^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 9 to get 4.

$$\frac{m^{4}}{m^{6}\left(m^{2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{m^{4}}{m^{6}m^{-8}}$$

To multiply powers of the same base, add their exponents. Add 6 and -8 to get -2.

$$\frac{m^{4}}{m^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 4 to get 6.

$$m^{6}$$

Expand

$$m^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\frac{\left(m^{3}\right)^{3}}{m^{5}}}{m^{6}\left(m^{2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{m^{9}}{m^{5}}}{m^{6}\left(m^{2}\right)^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 9 to get 4.

$$\frac{m^{4}}{m^{6}\left(m^{2}\right)^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.

$$\frac{m^{4}}{m^{6}m^{-8}}$$

To multiply powers of the same base, add their exponents. Add 6 and -8 to get -2.

$$\frac{m^{4}}{m^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 4 to get 6.

$$m^{6}$$