Solve frac{(2a^{2}c)^-3abc^41}{6a^6b^-3}

$$\frac { ( 2 a ^ { 2 } c ) ^ { - 3 } a b c ^ { 41 } } { 6 a ^ { 6 } b ^ { - 3 } }$$

Evaluate

$$\frac{b^{4}c^{38}}{48a^{11}}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{\left(2ca^{2}\right)^{-3}bc^{41}}{6b^{-3}a^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(2ca^{2}\right)^{-3}b^{4}c^{41}}{6a^{5}}$$

Expand \left(2ca^{2}\right)^{-3}.

$$\frac{2^{-3}c^{-3}\left(a^{2}\right)^{-3}b^{4}c^{41}}{6a^{5}}$$

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

$$\frac{2^{-3}c^{-3}a^{-6}b^{4}c^{41}}{6a^{5}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}c^{-3}a^{-6}b^{4}c^{41}}{6a^{5}}$$

To multiply powers of the same base, add their exponents. Add -3 and 41 to get 38.

$$\frac{\frac{1}{8}c^{38}a^{-6}b^{4}}{6a^{5}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{8}b^{4}c^{38}}{6a^{11}}$$

Expand

$$\frac{b^{4}c^{38}}{48a^{11}}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{\left(2ca^{2}\right)^{-3}bc^{41}}{6b^{-3}a^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(2ca^{2}\right)^{-3}b^{4}c^{41}}{6a^{5}}$$

Expand \left(2ca^{2}\right)^{-3}.

$$\frac{2^{-3}c^{-3}\left(a^{2}\right)^{-3}b^{4}c^{41}}{6a^{5}}$$

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

$$\frac{2^{-3}c^{-3}a^{-6}b^{4}c^{41}}{6a^{5}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}c^{-3}a^{-6}b^{4}c^{41}}{6a^{5}}$$

To multiply powers of the same base, add their exponents. Add -3 and 41 to get 38.

$$\frac{\frac{1}{8}c^{38}a^{-6}b^{4}}{6a^{5}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{8}b^{4}c^{38}}{6a^{11}}$$