Solve (5p ^ 2 * q ^ 3) ^ 2 * (6pq) + (4p * q ^ 2) ^ 3 * (- 2p ^ 2 * q) | 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

$$(5p^{2}q^{3})^{2}(6pq)+(4pq^{2})^{3}(-2p^{2}q)$$

Evaluate

$22p^{5}q^{7}$

Solution Steps

Expand $\left(5p^{2}q^{3}\right)^{2}$.

$$5^{2}\left(p^{2}\right)^{2}\left(q^{3}\right)^{2}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$5^{2}p^{4}\left(q^{3}\right)^{2}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$5^{2}p^{4}q^{6}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Calculate $5$ to the power of $2$ and get $25$.

$$25p^{4}q^{6}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Multiply $25$ and $6$ to get $150$.

$$150p^{4}q^{6}pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

To multiply powers of the same base, add their exponents. Add $4$ and $1$ to get $5$.

$$150p^{5}q^{6}q+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$150p^{5}q^{7}+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Expand $\left(4pq^{2}\right)^{3}$.

$$150p^{5}q^{7}+4^{3}p^{3}\left(q^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$150p^{5}q^{7}+4^{3}p^{3}q^{6}\left(-2\right)p^{2}q$$

Calculate $4$ to the power of $3$ and get $64$.

$$150p^{5}q^{7}+64p^{3}q^{6}\left(-2\right)p^{2}q$$

Multiply $64$ and $-2$ to get $-128$.

$$150p^{5}q^{7}-128p^{3}q^{6}p^{2}q$$

To multiply powers of the same base, add their exponents. Add $3$ and $2$ to get $5$.

$$150p^{5}q^{7}-128p^{5}q^{6}q$$

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

$$150p^{5}q^{7}-128p^{5}q^{7}$$

Combine $150p^{5}q^{7}$ and $-128p^{5}q^{7}$ to get $22p^{5}q^{7}$.

$$22p^{5}q^{7}$$

Expand

$22p^{5}q^{7}$

Solution Steps

Expand $\left(5p^{2}q^{3}\right)^{2}$.

$$5^{2}\left(p^{2}\right)^{2}\left(q^{3}\right)^{2}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$5^{2}p^{4}\left(q^{3}\right)^{2}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$5^{2}p^{4}q^{6}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Calculate $5$ to the power of $2$ and get $25$.

$$25p^{4}q^{6}\times 6pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Multiply $25$ and $6$ to get $150$.

$$150p^{4}q^{6}pq+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

To multiply powers of the same base, add their exponents. Add $4$ and $1$ to get $5$.

$$150p^{5}q^{6}q+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$150p^{5}q^{7}+\left(4pq^{2}\right)^{3}\left(-2\right)p^{2}q$$

Expand $\left(4pq^{2}\right)^{3}$.

$$150p^{5}q^{7}+4^{3}p^{3}\left(q^{2}\right)^{3}\left(-2\right)p^{2}q$$

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

$$150p^{5}q^{7}+4^{3}p^{3}q^{6}\left(-2\right)p^{2}q$$

Calculate $4$ to the power of $3$ and get $64$.

$$150p^{5}q^{7}+64p^{3}q^{6}\left(-2\right)p^{2}q$$

Multiply $64$ and $-2$ to get $-128$.

$$150p^{5}q^{7}-128p^{3}q^{6}p^{2}q$$

To multiply powers of the same base, add their exponents. Add $3$ and $2$ to get $5$.

$$150p^{5}q^{7}-128p^{5}q^{6}q$$

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

$$150p^{5}q^{7}-128p^{5}q^{7}$$

Combine $150p^{5}q^{7}$ and $-128p^{5}q^{7}$ to get $22p^{5}q^{7}$.

$$22p^{5}q^{7}$$