Solve (15a^3b/45b^8)^-2=

$$( \frac { 15 a ^ { 3 } b } { 45 b ^ { 8 } } ) ^ { - 2 } =$$

Evaluate

$$\frac{9b^{14}}{a^{6}}$$

Solution Steps

Cancel out 15b in both numerator and denominator.

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

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

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{a^{-6}}{\frac{1}{9}b^{-14}}$$

Expand

$$\frac{9b^{14}}{a^{6}}$$

Solution Steps

Cancel out 15b in both numerator and denominator.

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 7 and -2 to get -14.

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

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{a^{-6}}{\frac{1}{9}b^{-14}}$$