Solve [-3(a)^(3)(b)^(2)(c)^(4)(d)^(5)((a)^(4)b(c)^(3))((a)^(4)b(c)^(3))^(3)]4 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$[-3 { a }^{ 3 } { b }^{ 2 } { c }^{ 4 } { d }^{ 5 } ( { a }^{ 4 } b { c }^{ 3 } ) { \left( { a }^{ 4 } b { c }^{ 3 } \right) }^{ 3 } ]4$$

Evaluate

$-12d^{5}b^{6}c^{16}a^{19}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $3$ and $4$ to get $7$.

$$-3a^{7}b^{2}c^{4}d^{5}bc^{3}\left(a^{4}bc^{3}\right)^{3}\times 4$$

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

$$-3a^{7}b^{3}c^{4}d^{5}c^{3}\left(a^{4}bc^{3}\right)^{3}\times 4$$

To multiply powers of the same base, add their exponents. Add $4$ and $3$ to get $7$.

$$-3a^{7}b^{3}c^{7}d^{5}\left(a^{4}bc^{3}\right)^{3}\times 4$$

Expand $\left(a^{4}bc^{3}\right)^{3}$.

$$-3a^{7}b^{3}c^{7}d^{5}\left(a^{4}\right)^{3}b^{3}\left(c^{3}\right)^{3}\times 4$$

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

$$-3a^{7}b^{3}c^{7}d^{5}a^{12}b^{3}\left(c^{3}\right)^{3}\times 4$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$-3a^{7}b^{3}c^{7}d^{5}a^{12}b^{3}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $7$ and $12$ to get $19$.

$$-3a^{19}b^{3}c^{7}d^{5}b^{3}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $3$ and $3$ to get $6$.

$$-3a^{19}b^{6}c^{7}d^{5}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $7$ and $9$ to get $16$.

$$-3a^{19}b^{6}c^{16}d^{5}\times 4$$

Multiply $-3$ and $4$ to get $-12$.

$$-12a^{19}b^{6}c^{16}d^{5}$$

Expand

$-12d^{5}b^{6}c^{16}a^{19}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $3$ and $4$ to get $7$.

$$-3a^{7}b^{2}c^{4}d^{5}bc^{3}\left(a^{4}bc^{3}\right)^{3}\times 4$$

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

$$-3a^{7}b^{3}c^{4}d^{5}c^{3}\left(a^{4}bc^{3}\right)^{3}\times 4$$

To multiply powers of the same base, add their exponents. Add $4$ and $3$ to get $7$.

$$-3a^{7}b^{3}c^{7}d^{5}\left(a^{4}bc^{3}\right)^{3}\times 4$$

Expand $\left(a^{4}bc^{3}\right)^{3}$.

$$-3a^{7}b^{3}c^{7}d^{5}\left(a^{4}\right)^{3}b^{3}\left(c^{3}\right)^{3}\times 4$$

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

$$-3a^{7}b^{3}c^{7}d^{5}a^{12}b^{3}\left(c^{3}\right)^{3}\times 4$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$-3a^{7}b^{3}c^{7}d^{5}a^{12}b^{3}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $7$ and $12$ to get $19$.

$$-3a^{19}b^{3}c^{7}d^{5}b^{3}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $3$ and $3$ to get $6$.

$$-3a^{19}b^{6}c^{7}d^{5}c^{9}\times 4$$

To multiply powers of the same base, add their exponents. Add $7$ and $9$ to get $16$.

$$-3a^{19}b^{6}c^{16}d^{5}\times 4$$

Multiply $-3$ and $4$ to get $-12$.

$$-12a^{19}b^{6}c^{16}d^{5}$$