Solve left(a^-3right)^2{left(left(a^4right)^-6/{left({a^-2right)}^3}right)}^-5

$${ \left( { a }^{ -3 } \right) }^{ 2 } { \left( \frac{ { \left( { a }^{ 4 } \right) }^{ -6 } }{ { \left( { a }^{ -2 } \right) }^{ 3 } } \right) }^{ -5 }$$

Evaluate

$$a^{84}$$

Solution Steps

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

$$a^{-6}\times \left(\frac{\left(a^{4}\right)^{-6}}{\left(a^{-2}\right)^{3}}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -6 to get -24.

$$a^{-6}\times \left(\frac{a^{-24}}{\left(a^{-2}\right)^{3}}\right)^{-5}$$

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

$$a^{-6}\times \left(\frac{a^{-24}}{a^{-6}}\right)^{-5}$$

Rewrite a^{-6} as a^{-24}a^{18}. Cancel out a^{-24} in both numerator and denominator.

$$a^{-6}\times \left(\frac{1}{a^{18}}\right)^{-5}$$

To raise \frac{1}{a^{18}} to a power, raise both numerator and denominator to the power and then divide.

$$a^{-6}\times \frac{1^{-5}}{\left(a^{18}\right)^{-5}}$$

Express a^{-6}\times \frac{1^{-5}}{\left(a^{18}\right)^{-5}} as a single fraction.

$$\frac{a^{-6}\times 1^{-5}}{\left(a^{18}\right)^{-5}}$$

To raise a power to another power, multiply the exponents. Multiply 18 and -5 to get -90.

$$\frac{a^{-6}\times 1^{-5}}{a^{-90}}$$

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

$$1^{-5}a^{84}$$

Calculate 1 to the power of -5 and get 1.

$$1a^{84}$$

For any term t, t\times 1=t and 1t=t.

$$a^{84}$$

Expand

$$a^{84}$$

Solution Steps

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

$$a^{-6}\times \left(\frac{\left(a^{4}\right)^{-6}}{\left(a^{-2}\right)^{3}}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -6 to get -24.

$$a^{-6}\times \left(\frac{a^{-24}}{\left(a^{-2}\right)^{3}}\right)^{-5}$$

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

$$a^{-6}\times \left(\frac{a^{-24}}{a^{-6}}\right)^{-5}$$

Rewrite a^{-6} as a^{-24}a^{18}. Cancel out a^{-24} in both numerator and denominator.

$$a^{-6}\times \left(\frac{1}{a^{18}}\right)^{-5}$$

To raise \frac{1}{a^{18}} to a power, raise both numerator and denominator to the power and then divide.

$$a^{-6}\times \frac{1^{-5}}{\left(a^{18}\right)^{-5}}$$

Express a^{-6}\times \frac{1^{-5}}{\left(a^{18}\right)^{-5}} as a single fraction.

$$\frac{a^{-6}\times 1^{-5}}{\left(a^{18}\right)^{-5}}$$

To raise a power to another power, multiply the exponents. Multiply 18 and -5 to get -90.

$$\frac{a^{-6}\times 1^{-5}}{a^{-90}}$$

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

$$1^{-5}a^{84}$$

Calculate 1 to the power of -5 and get 1.

$$1a^{84}$$

For any term t, t\times 1=t and 1t=t.

$$a^{84}$$