Solve [(-3/4a^2bc)^3*(-3/4abc)]^4

$$[ ( - \frac { 3 } { 4 } a ^ { 2 } b c ) ^ { 3 } \cdot ( - \frac { 3 } { 4 } a b c ) ] ^ { 4 }$$

Evaluate

$$\frac{43046721a^{28}\left(bc\right)^{16}}{4294967296}$$

Solution Steps

Expand \left(-\frac{3}{4}a^{2}bc\right)^{3}.

$$\left(\left(-\frac{3}{4}\right)^{3}\left(a^{2}\right)^{3}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

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

$$\left(\left(-\frac{3}{4}\right)^{3}a^{6}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

Calculate -\frac{3}{4} to the power of 3 and get -\frac{27}{64}.

$$\left(-\frac{27}{64}a^{6}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

Multiply -\frac{27}{64} and -\frac{3}{4} to get \frac{81}{256}.

$$\left(\frac{81}{256}a^{6}b^{3}c^{3}abc\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(\frac{81}{256}a^{7}b^{3}c^{3}bc\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{81}{256}a^{7}b^{4}c^{3}c\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{81}{256}a^{7}b^{4}c^{4}\right)^{4}$$

Expand \left(\frac{81}{256}a^{7}b^{4}c^{4}\right)^{4}.

$$\left(\frac{81}{256}\right)^{4}\left(a^{7}\right)^{4}\left(b^{4}\right)^{4}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(\frac{81}{256}\right)^{4}a^{28}\left(b^{4}\right)^{4}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{81}{256}\right)^{4}a^{28}b^{16}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{81}{256}\right)^{4}a^{28}b^{16}c^{16}$$

Calculate \frac{81}{256} to the power of 4 and get \frac{43046721}{4294967296}.

$$\frac{43046721}{4294967296}a^{28}b^{16}c^{16}$$

Expand

$$\frac{43046721a^{28}\left(bc\right)^{16}}{4294967296}$$

Solution Steps

Expand \left(-\frac{3}{4}a^{2}bc\right)^{3}.

$$\left(\left(-\frac{3}{4}\right)^{3}\left(a^{2}\right)^{3}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

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

$$\left(\left(-\frac{3}{4}\right)^{3}a^{6}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

Calculate -\frac{3}{4} to the power of 3 and get -\frac{27}{64}.

$$\left(-\frac{27}{64}a^{6}b^{3}c^{3}\left(-\frac{3}{4}\right)abc\right)^{4}$$

Multiply -\frac{27}{64} and -\frac{3}{4} to get \frac{81}{256}.

$$\left(\frac{81}{256}a^{6}b^{3}c^{3}abc\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(\frac{81}{256}a^{7}b^{3}c^{3}bc\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{81}{256}a^{7}b^{4}c^{3}c\right)^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{81}{256}a^{7}b^{4}c^{4}\right)^{4}$$

Expand \left(\frac{81}{256}a^{7}b^{4}c^{4}\right)^{4}.

$$\left(\frac{81}{256}\right)^{4}\left(a^{7}\right)^{4}\left(b^{4}\right)^{4}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(\frac{81}{256}\right)^{4}a^{28}\left(b^{4}\right)^{4}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{81}{256}\right)^{4}a^{28}b^{16}\left(c^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{81}{256}\right)^{4}a^{28}b^{16}c^{16}$$

Calculate \frac{81}{256} to the power of 4 and get \frac{43046721}{4294967296}.

$$\frac{43046721}{4294967296}a^{28}b^{16}c^{16}$$