Solve (frac{27a^{5}b^{3}}{14a^{-2}b})(frac{3a^{-5}b^0}{7b^2a^-1})^-3

$$( \frac { 27 a ^ { 5 } b ^ { 3 } } { 14 a ^ { - 2 } b } ) ( \frac { 3 a ^ { - 5 } b ^ { 0 } } { 7 b ^ { 2 } a ^ { - 1 } } ) ^ { - 3 }$$

Evaluate

$$\frac{49b^{8}a^{19}}{2}$$

Solution Steps

Cancel out b in both numerator and denominator.

$$\frac{27b^{2}a^{5}}{14a^{-2}}\times \left(\frac{3a^{-5}b^{0}}{7b^{2}a^{-1}}\right)^{-3}$$

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

$$\frac{27b^{2}a^{7}}{14}\times \left(\frac{3a^{-5}b^{0}}{7b^{2}a^{-1}}\right)^{-3}$$

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

$$\frac{27b^{2}a^{7}}{14}\times \left(\frac{3}{7b^{2}a^{4}}\right)^{-3}$$

To raise \frac{3}{7b^{2}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{27b^{2}a^{7}}{14}\times \frac{3^{-3}}{\left(7b^{2}a^{4}\right)^{-3}}$$

Multiply \frac{27b^{2}a^{7}}{14} times \frac{3^{-3}}{\left(7b^{2}a^{4}\right)^{-3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27b^{2}a^{7}\times 3^{-3}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{27b^{2}a^{7}\times \frac{1}{27}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Multiply 27 and \frac{1}{27} to get 1.

$$\frac{b^{2}a^{7}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Expand \left(7b^{2}a^{4}\right)^{-3}.

$$\frac{b^{2}a^{7}}{14\times 7^{-3}\left(b^{2}\right)^{-3}\left(a^{4}\right)^{-3}}$$

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

$$\frac{b^{2}a^{7}}{14\times 7^{-3}b^{-6}\left(a^{4}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{b^{2}a^{7}}{14\times 7^{-3}b^{-6}a^{-12}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{b^{2}a^{7}}{14\times \frac{1}{343}b^{-6}a^{-12}}$$

Multiply 14 and \frac{1}{343} to get \frac{2}{49}.

$$\frac{b^{2}a^{7}}{\frac{2}{49}b^{-6}a^{-12}}$$

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

$$\frac{b^{8}a^{19}}{\frac{2}{49}}$$

Divide b^{8}a^{19} by \frac{2}{49} by multiplying b^{8}a^{19} by the reciprocal of \frac{2}{49}.

$$\frac{b^{8}a^{19}\times 49}{2}$$

Expand

$$\frac{49b^{8}a^{19}}{2}$$

Solution Steps

Cancel out b in both numerator and denominator.

$$\frac{27b^{2}a^{5}}{14a^{-2}}\times \left(\frac{3a^{-5}b^{0}}{7b^{2}a^{-1}}\right)^{-3}$$

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

$$\frac{27b^{2}a^{7}}{14}\times \left(\frac{3a^{-5}b^{0}}{7b^{2}a^{-1}}\right)^{-3}$$

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

$$\frac{27b^{2}a^{7}}{14}\times \left(\frac{3}{7b^{2}a^{4}}\right)^{-3}$$

To raise \frac{3}{7b^{2}a^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{27b^{2}a^{7}}{14}\times \frac{3^{-3}}{\left(7b^{2}a^{4}\right)^{-3}}$$

Multiply \frac{27b^{2}a^{7}}{14} times \frac{3^{-3}}{\left(7b^{2}a^{4}\right)^{-3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27b^{2}a^{7}\times 3^{-3}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{27b^{2}a^{7}\times \frac{1}{27}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Multiply 27 and \frac{1}{27} to get 1.

$$\frac{b^{2}a^{7}}{14\times \left(7b^{2}a^{4}\right)^{-3}}$$

Expand \left(7b^{2}a^{4}\right)^{-3}.

$$\frac{b^{2}a^{7}}{14\times 7^{-3}\left(b^{2}\right)^{-3}\left(a^{4}\right)^{-3}}$$

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

$$\frac{b^{2}a^{7}}{14\times 7^{-3}b^{-6}\left(a^{4}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{b^{2}a^{7}}{14\times 7^{-3}b^{-6}a^{-12}}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$\frac{b^{2}a^{7}}{14\times \frac{1}{343}b^{-6}a^{-12}}$$

Multiply 14 and \frac{1}{343} to get \frac{2}{49}.

$$\frac{b^{2}a^{7}}{\frac{2}{49}b^{-6}a^{-12}}$$

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

$$\frac{b^{8}a^{19}}{\frac{2}{49}}$$

Divide b^{8}a^{19} by \frac{2}{49} by multiplying b^{8}a^{19} by the reciprocal of \frac{2}{49}.

$$\frac{b^{8}a^{19}\times 49}{2}$$