Solve frac{(5a^{2})(6p^3)}{(2a^3)(5^-1p)^-2}

$$\frac { ( 5 a ^ { 2 } ) ( 6 p ^ { 3 } ) } { ( 2 a ^ { 3 } ) ( 5 ^ { - 1 } p ) ^ { - 2 } }$$

Evaluate

$$\frac{3p^{5}}{5a}$$

Solution Steps

Cancel out 2a^{2} in both numerator and denominator.

$$\frac{3\times 5p^{3}}{\left(\frac{1}{5}p\right)^{-2}a}$$

Multiply 3 and 5 to get 15.

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

Expand \left(\frac{1}{5}p\right)^{-2}.

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

Calculate \frac{1}{5} to the power of -2 and get 25.

$$\frac{15p^{3}}{25p^{-2}a}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3p^{3}}{5p^{-2}a}$$

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

$$\frac{3p^{5}}{5a}$$

Expand

$$\frac{3p^{5}}{5a}$$

Solution Steps

Cancel out 2a^{2} in both numerator and denominator.

$$\frac{3\times 5p^{3}}{\left(\frac{1}{5}p\right)^{-2}a}$$

Multiply 3 and 5 to get 15.

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

Expand \left(\frac{1}{5}p\right)^{-2}.

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

Calculate \frac{1}{5} to the power of -2 and get 25.

$$\frac{15p^{3}}{25p^{-2}a}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3p^{3}}{5p^{-2}a}$$

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

$$\frac{3p^{5}}{5a}$$