Solve (q^2)^3*(q^5/q)^2

$$( q ^ { 2 } ) ^ { 3 } \times ( \frac { q ^ { 5 } } { q } ) ^ { 2 }$$

Evaluate

$$q^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$q^{6}\times \left(\frac{q^{5}}{q}\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 5 to get 4.

$$q^{6}\left(q^{4}\right)^{2}$$

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

$$q^{6}q^{8}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$q^{14}$$

Expand

$$q^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$q^{6}\times \left(\frac{q^{5}}{q}\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 5 to get 4.

$$q^{6}\left(q^{4}\right)^{2}$$

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

$$q^{6}q^{8}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$q^{14}$$