Solve ba^4*(2ba^4)^-3quad8

$$b a ^ { 4 } \times ( 2 b a ^ { 4 } ) ^ { - 3 } \quad 8$$

Evaluate

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

Solution Steps

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

$$ba^{4}\times 2^{-3}b^{-3}\left(a^{4}\right)^{-3}\times 8$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$ba^{4}\times 2^{-3}b^{-3}a^{-12}\times 8$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$ba^{4}\times \frac{1}{8}b^{-3}a^{-12}\times 8$$

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$b^{-2}a^{4}\times \frac{1}{8}a^{-12}\times 8$$

To multiply powers of the same base, add their exponents. Add 4 and -12 to get -8.

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

Multiply \frac{1}{8} and 8 to get 1.

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

Expand

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

Solution Steps

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

$$ba^{4}\times 2^{-3}b^{-3}\left(a^{4}\right)^{-3}\times 8$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$ba^{4}\times 2^{-3}b^{-3}a^{-12}\times 8$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$ba^{4}\times \frac{1}{8}b^{-3}a^{-12}\times 8$$

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$b^{-2}a^{4}\times \frac{1}{8}a^{-12}\times 8$$

To multiply powers of the same base, add their exponents. Add 4 and -12 to get -8.

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

Multiply \frac{1}{8} and 8 to get 1.

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