Solve (frac{a^{3}}{b^{6}c^{7}})^{-7}:(a^-3b^4/c^2)^2=

$$( \frac { a ^ { 3 } } { b ^ { 6 } c ^ { 7 } } ) ^ { - 7 } : ( \frac { a ^ { - 3 } b ^ { 4 } } { c ^ { 2 } } ) ^ { 2 } =$$

Evaluate

$$\frac{b^{34}c^{53}}{a^{15}}$$

Solution Steps

To raise \frac{a^{3}}{b^{6}c^{7}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Divide \frac{\left(a^{3}\right)^{-7}}{\left(b^{6}c^{7}\right)^{-7}} by \frac{\left(a^{-3}b^{4}\right)^{2}}{\left(c^{2}\right)^{2}} by multiplying \frac{\left(a^{3}\right)^{-7}}{\left(b^{6}c^{7}\right)^{-7}} by the reciprocal of \frac{\left(a^{-3}b^{4}\right)^{2}}{\left(c^{2}\right)^{2}}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -7 to get -21.

$$\frac{a^{-21}\left(c^{2}\right)^{2}}{\left(b^{6}c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{-21}c^{4}}{\left(b^{6}c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

Expand \left(b^{6}c^{7}\right)^{-7}.

$$\frac{a^{-21}c^{4}}{\left(b^{6}\right)^{-7}\left(c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -7 to get -42.

$$\frac{a^{-21}c^{4}}{b^{-42}\left(c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -7 to get -49.

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}\left(a^{-3}b^{4}\right)^{2}}$$

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

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}\left(a^{-3}\right)^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}a^{-6}\left(b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}a^{-6}b^{8}}$$

To multiply powers of the same base, add their exponents. Add -42 and 8 to get -34.

$$\frac{a^{-21}c^{4}}{b^{-34}c^{-49}a^{-6}}$$

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

$$\frac{a^{-21}c^{53}}{b^{-34}a^{-6}}$$

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

$$\frac{c^{53}}{b^{-34}a^{15}}$$

Expand

$$\frac{b^{34}c^{53}}{a^{15}}$$

Solution Steps

To raise \frac{a^{3}}{b^{6}c^{7}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Divide \frac{\left(a^{3}\right)^{-7}}{\left(b^{6}c^{7}\right)^{-7}} by \frac{\left(a^{-3}b^{4}\right)^{2}}{\left(c^{2}\right)^{2}} by multiplying \frac{\left(a^{3}\right)^{-7}}{\left(b^{6}c^{7}\right)^{-7}} by the reciprocal of \frac{\left(a^{-3}b^{4}\right)^{2}}{\left(c^{2}\right)^{2}}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -7 to get -21.

$$\frac{a^{-21}\left(c^{2}\right)^{2}}{\left(b^{6}c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{a^{-21}c^{4}}{\left(b^{6}c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

Expand \left(b^{6}c^{7}\right)^{-7}.

$$\frac{a^{-21}c^{4}}{\left(b^{6}\right)^{-7}\left(c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -7 to get -42.

$$\frac{a^{-21}c^{4}}{b^{-42}\left(c^{7}\right)^{-7}\left(a^{-3}b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -7 to get -49.

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}\left(a^{-3}b^{4}\right)^{2}}$$

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

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}\left(a^{-3}\right)^{2}\left(b^{4}\right)^{2}}$$

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

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}a^{-6}\left(b^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{-21}c^{4}}{b^{-42}c^{-49}a^{-6}b^{8}}$$

To multiply powers of the same base, add their exponents. Add -42 and 8 to get -34.

$$\frac{a^{-21}c^{4}}{b^{-34}c^{-49}a^{-6}}$$

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

$$\frac{a^{-21}c^{53}}{b^{-34}a^{-6}}$$

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

$$\frac{c^{53}}{b^{-34}a^{15}}$$