Solve frac{49a^{8}}{b^16}(7a^9b^-5)^2

$$\frac { 49 a ^ { 8 } } { b ^ { 16 } } ( 7 a ^ { 9 } b ^ { - 5 } ) ^ { 2 }$$

Evaluate

$$2401\times \left(\frac{a}{b}\right)^{26}$$

Solution Steps

Expand \left(7a^{9}b^{-5}\right)^{2}.

$$\frac{49a^{8}}{b^{16}}\times 7^{2}\left(a^{9}\right)^{2}\left(b^{-5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{49a^{8}}{b^{16}}\times 7^{2}a^{18}\left(b^{-5}\right)^{2}$$

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

$$\frac{49a^{8}}{b^{16}}\times 7^{2}a^{18}b^{-10}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49a^{8}}{b^{16}}\times 49a^{18}b^{-10}$$

Express \frac{49a^{8}}{b^{16}}\times 49 as a single fraction.

$$\frac{49a^{8}\times 49}{b^{16}}a^{18}b^{-10}$$

Express \frac{49a^{8}\times 49}{b^{16}}a^{18} as a single fraction.

$$\frac{49a^{8}\times 49a^{18}}{b^{16}}b^{-10}$$

Express \frac{49a^{8}\times 49a^{18}}{b^{16}}b^{-10} as a single fraction.

$$\frac{49a^{8}\times 49a^{18}b^{-10}}{b^{16}}$$

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

$$\frac{49\times 49a^{8}a^{18}}{b^{26}}$$

To multiply powers of the same base, add their exponents. Add 8 and 18 to get 26.

$$\frac{49\times 49a^{26}}{b^{26}}$$

Multiply 49 and 49 to get 2401.

$$\frac{2401a^{26}}{b^{26}}$$

Expand

$$2401\times \left(\frac{a}{b}\right)^{26}$$

Solution Steps

Expand \left(7a^{9}b^{-5}\right)^{2}.

$$\frac{49a^{8}}{b^{16}}\times 7^{2}\left(a^{9}\right)^{2}\left(b^{-5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{49a^{8}}{b^{16}}\times 7^{2}a^{18}\left(b^{-5}\right)^{2}$$

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

$$\frac{49a^{8}}{b^{16}}\times 7^{2}a^{18}b^{-10}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49a^{8}}{b^{16}}\times 49a^{18}b^{-10}$$

Express \frac{49a^{8}}{b^{16}}\times 49 as a single fraction.

$$\frac{49a^{8}\times 49}{b^{16}}a^{18}b^{-10}$$

Express \frac{49a^{8}\times 49}{b^{16}}a^{18} as a single fraction.

$$\frac{49a^{8}\times 49a^{18}}{b^{16}}b^{-10}$$

Express \frac{49a^{8}\times 49a^{18}}{b^{16}}b^{-10} as a single fraction.

$$\frac{49a^{8}\times 49a^{18}b^{-10}}{b^{16}}$$

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

$$\frac{49\times 49a^{8}a^{18}}{b^{26}}$$

To multiply powers of the same base, add their exponents. Add 8 and 18 to get 26.

$$\frac{49\times 49a^{26}}{b^{26}}$$

Multiply 49 and 49 to get 2401.

$$\frac{2401a^{26}}{b^{26}}$$