Solve (14a^-3b/2a^-7)^-2

$$( \frac { 14 a ^ { - 3 } b } { 2 a ^ { - 7 } } ) ^ { - 2 }$$

Evaluate

$$\frac{1}{49b^{2}a^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(7ba^{4}\right)^{-2}$$

Expand \left(7ba^{4}\right)^{-2}.

$$7^{-2}b^{-2}\left(a^{4}\right)^{-2}$$

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

$$7^{-2}b^{-2}a^{-8}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{1}{49}b^{-2}a^{-8}$$

Expand

$$\frac{1}{49b^{2}a^{8}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

$$\left(7ba^{4}\right)^{-2}$$

Expand \left(7ba^{4}\right)^{-2}.

$$7^{-2}b^{-2}\left(a^{4}\right)^{-2}$$

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

$$7^{-2}b^{-2}a^{-8}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{1}{49}b^{-2}a^{-8}$$