Solve frac{(3y^{5})^{4}}{(y^{-5})^{-3}*(y^{-2})^{-1}}-frac{(4y^{2})^{3}}{(y^-3)^-3}-15(y^3)^-1

$$\frac { ( 3 y ^ { 5 } ) ^ { 4 } } { ( y ^ { - 5 } ) ^ { - 3 } \cdot ( y ^ { - 2 } ) ^ { - 1 } } - \frac { ( 4 y ^ { 2 } ) ^ { 3 } } { ( y ^ { - 3 } ) ^ { - 3 } } - 15 ( y ^ { 3 } ) ^ { - 1 }$$

Evaluate

$$81y^{3}-\frac{79}{y^{3}}$$

Short Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{\left(3y^{5}\right)^{4}}{y^{15}\left(y^{-2}\right)^{-1}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -1 to get 2.

$$\frac{\left(3y^{5}\right)^{4}}{y^{15}y^{2}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

To multiply powers of the same base, add their exponents. Add 15 and 2 to get 17.

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

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

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15\left(y^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Expand \left(3y^{5}\right)^{4}.

$$\frac{3^{4}\left(y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{3^{4}y^{20}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81y^{20}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Cancel out y^{17} in both numerator and denominator.

$$81y^{3}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Expand \left(4y^{2}\right)^{3}.

$$81y^{3}-\frac{4^{3}\left(y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

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

$$81y^{3}-\frac{4^{3}y^{6}}{y^{9}}-15y^{-3}$$

Calculate 4 to the power of 3 and get 64.

$$81y^{3}-\frac{64y^{6}}{y^{9}}-15y^{-3}$$

Cancel out y^{6} in both numerator and denominator.

$$81y^{3}-\frac{64}{y^{3}}-15y^{-3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81y^{3} times \frac{y^{3}}{y^{3}}.

$$\frac{81y^{3}y^{3}}{y^{3}}-\frac{64}{y^{3}}-15y^{-3}$$

Since \frac{81y^{3}y^{3}}{y^{3}} and \frac{64}{y^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81y^{3}y^{3}-64}{y^{3}}-15y^{-3}$$

Do the multiplications in 81y^{3}y^{3}-64.

$$\frac{81y^{6}-64}{y^{3}}-15y^{-3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -15y^{-3} times \frac{y^{3}}{y^{3}}.

$$\frac{81y^{6}-64}{y^{3}}+\frac{-15y^{-3}y^{3}}{y^{3}}$$

Since \frac{81y^{6}-64}{y^{3}} and \frac{-15y^{-3}y^{3}}{y^{3}} have the same denominator, add them by adding their numerators.

$$\frac{81y^{6}-64-15y^{-3}y^{3}}{y^{3}}$$

Do the multiplications in 81y^{6}-64-15y^{-3}y^{3}.

$$\frac{81y^{6}-64-15}{y^{3}}$$

Combine like terms in 81y^{6}-64-15.

$$\frac{81y^{6}-79}{y^{3}}$$

Expand

$$81y^{3}-\frac{79}{y^{3}}$$

Short Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -3 to get 15.

$$\frac{\left(3y^{5}\right)^{4}}{y^{15}\left(y^{-2}\right)^{-1}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -1 to get 2.

$$\frac{\left(3y^{5}\right)^{4}}{y^{15}y^{2}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

To multiply powers of the same base, add their exponents. Add 15 and 2 to get 17.

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{\left(y^{-3}\right)^{-3}}-15\left(y^{3}\right)^{-1}$$

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

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15\left(y^{3}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

$$\frac{\left(3y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Expand \left(3y^{5}\right)^{4}.

$$\frac{3^{4}\left(y^{5}\right)^{4}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{3^{4}y^{20}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81y^{20}}{y^{17}}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Cancel out y^{17} in both numerator and denominator.

$$81y^{3}-\frac{\left(4y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

Expand \left(4y^{2}\right)^{3}.

$$81y^{3}-\frac{4^{3}\left(y^{2}\right)^{3}}{y^{9}}-15y^{-3}$$

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

$$81y^{3}-\frac{4^{3}y^{6}}{y^{9}}-15y^{-3}$$

Calculate 4 to the power of 3 and get 64.

$$81y^{3}-\frac{64y^{6}}{y^{9}}-15y^{-3}$$

Cancel out y^{6} in both numerator and denominator.

$$81y^{3}-\frac{64}{y^{3}}-15y^{-3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81y^{3} times \frac{y^{3}}{y^{3}}.

$$\frac{81y^{3}y^{3}}{y^{3}}-\frac{64}{y^{3}}-15y^{-3}$$

Since \frac{81y^{3}y^{3}}{y^{3}} and \frac{64}{y^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81y^{3}y^{3}-64}{y^{3}}-15y^{-3}$$

Do the multiplications in 81y^{3}y^{3}-64.

$$\frac{81y^{6}-64}{y^{3}}-15y^{-3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -15y^{-3} times \frac{y^{3}}{y^{3}}.

$$\frac{81y^{6}-64}{y^{3}}+\frac{-15y^{-3}y^{3}}{y^{3}}$$

Since \frac{81y^{6}-64}{y^{3}} and \frac{-15y^{-3}y^{3}}{y^{3}} have the same denominator, add them by adding their numerators.

$$\frac{81y^{6}-64-15y^{-3}y^{3}}{y^{3}}$$

Do the multiplications in 81y^{6}-64-15y^{-3}y^{3}.

$$\frac{81y^{6}-64-15}{y^{3}}$$

Combine like terms in 81y^{6}-64-15.

$$\frac{81y^{6}-79}{y^{3}}$$