Solve (a^{2}*b^{2})^-5:(a^-1:9^-5)^2

$$( a ^ { 2 } \cdot b ^ { 2 } ) ^ { - 5 } : ( a ^ { - 1 } : 9 ^ { - 5 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{3486784401a^{8}b^{10}}$$

Solution Steps

Expand \left(a^{2}b^{2}\right)^{-5}.

$$\frac{\left(a^{2}\right)^{-5}\left(b^{2}\right)^{-5}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\frac{a^{-10}\left(b^{2}\right)^{-5}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\frac{a^{-10}b^{-10}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

Calculate 9 to the power of -5 and get \frac{1}{59049}.

$$\frac{a^{-10}b^{-10}}{\left(\frac{a^{-1}}{\frac{1}{59049}}\right)^{2}}$$

Divide a^{-1} by \frac{1}{59049} by multiplying a^{-1} by the reciprocal of \frac{1}{59049}.

$$\frac{a^{-10}b^{-10}}{\left(a^{-1}\times 59049\right)^{2}}$$

Expand \left(a^{-1}\times 59049\right)^{2}.

$$\frac{a^{-10}b^{-10}}{\left(a^{-1}\right)^{2}\times 59049^{2}}$$

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

$$\frac{a^{-10}b^{-10}}{a^{-2}\times 59049^{2}}$$

Calculate 59049 to the power of 2 and get 3486784401.

$$\frac{a^{-10}b^{-10}}{a^{-2}\times 3486784401}$$

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

$$\frac{b^{-10}}{3486784401a^{8}}$$

Expand

$$\frac{1}{3486784401a^{8}b^{10}}$$

Solution Steps

Expand \left(a^{2}b^{2}\right)^{-5}.

$$\frac{\left(a^{2}\right)^{-5}\left(b^{2}\right)^{-5}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\frac{a^{-10}\left(b^{2}\right)^{-5}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.

$$\frac{a^{-10}b^{-10}}{\left(\frac{a^{-1}}{9^{-5}}\right)^{2}}$$

Calculate 9 to the power of -5 and get \frac{1}{59049}.

$$\frac{a^{-10}b^{-10}}{\left(\frac{a^{-1}}{\frac{1}{59049}}\right)^{2}}$$

Divide a^{-1} by \frac{1}{59049} by multiplying a^{-1} by the reciprocal of \frac{1}{59049}.

$$\frac{a^{-10}b^{-10}}{\left(a^{-1}\times 59049\right)^{2}}$$

Expand \left(a^{-1}\times 59049\right)^{2}.

$$\frac{a^{-10}b^{-10}}{\left(a^{-1}\right)^{2}\times 59049^{2}}$$

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

$$\frac{a^{-10}b^{-10}}{a^{-2}\times 59049^{2}}$$

Calculate 59049 to the power of 2 and get 3486784401.

$$\frac{a^{-10}b^{-10}}{a^{-2}\times 3486784401}$$

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

$$\frac{b^{-10}}{3486784401a^{8}}$$