Type a math problem

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Type a math problem

Evaluate

288a^{2}b^{7}c^{10}

$288a_{2}b_{7}c_{10}$

Solution Steps

(2a \cdot 3b^2)^2 \cdot c \cdot (2bc^3)^3

$(2a⋅3b_{2})_{2}⋅c⋅(2bc_{3})_{3}$

Multiply 2 and 3 to get 6.

Multiply $2$ and $3$ to get $6$.

\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

$(6ab_{2})_{2}c×(2bc_{3})_{3}$

Expand \left(6ab^{2}\right)^{2}.

Expand $(6ab_{2})_{2}$.

6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

$6_{2}a_{2}(b_{2})_{2}c×(2bc_{3})_{3}$

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

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

6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

$6_{2}a_{2}b_{4}c×(2bc_{3})_{3}$

Calculate 6 to the power of 2 and get 36.

Calculate $6$ to the power of $2$ and get $36$.

36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

$36a_{2}b_{4}c×(2bc_{3})_{3}$

Expand \left(2bc^{3}\right)^{3}.

Expand $(2bc_{3})_{3}$.

36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}

$36a_{2}b_{4}c×2_{3}b_{3}(c_{3})_{3}$

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

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

36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}

$36a_{2}b_{4}c×2_{3}b_{3}c_{9}$

Calculate 2 to the power of 3 and get 8.

Calculate $2$ to the power of $3$ and get $8$.

36a^{2}b^{4}c\times 8b^{3}c^{9}

$36a_{2}b_{4}c×8b_{3}c_{9}$

Multiply 36 and 8 to get 288.

Multiply $36$ and $8$ to get $288$.

288a^{2}b^{4}cb^{3}c^{9}

$288a_{2}b_{4}cb_{3}c_{9}$

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

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

288a^{2}b^{7}cc^{9}

$288a_{2}b_{7}cc_{9}$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

To multiply powers of the same base, add their exponents. Add $1$ and $9$ to get $10$.

288a^{2}b^{7}c^{10}

$288a_{2}b_{7}c_{10}$

Expand

288a^{2}b^{7}c^{10}

$288a_{2}b_{7}c_{10}$

Solution Steps

(2a \cdot 3b^2)^2 \cdot c \cdot (2bc^3)^3

$(2a⋅3b_{2})_{2}⋅c⋅(2bc_{3})_{3}$

Multiply 2 and 3 to get 6.

Multiply $2$ and $3$ to get $6$.

\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

$(6ab_{2})_{2}c×(2bc_{3})_{3}$

Expand \left(6ab^{2}\right)^{2}.

Expand $(6ab_{2})_{2}$.

6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

$6_{2}a_{2}(b_{2})_{2}c×(2bc_{3})_{3}$

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

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

6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

$6_{2}a_{2}b_{4}c×(2bc_{3})_{3}$

Calculate 6 to the power of 2 and get 36.

Calculate $6$ to the power of $2$ and get $36$.

36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

$36a_{2}b_{4}c×(2bc_{3})_{3}$

Expand \left(2bc^{3}\right)^{3}.

Expand $(2bc_{3})_{3}$.

36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}

$36a_{2}b_{4}c×2_{3}b_{3}(c_{3})_{3}$

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

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

36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}

$36a_{2}b_{4}c×2_{3}b_{3}c_{9}$

Calculate 2 to the power of 3 and get 8.

Calculate $2$ to the power of $3$ and get $8$.

36a^{2}b^{4}c\times 8b^{3}c^{9}

$36a_{2}b_{4}c×8b_{3}c_{9}$

Multiply 36 and 8 to get 288.

Multiply $36$ and $8$ to get $288$.

288a^{2}b^{4}cb^{3}c^{9}

$288a_{2}b_{4}cb_{3}c_{9}$

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

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

288a^{2}b^{7}cc^{9}

$288a_{2}b_{7}cc_{9}$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

To multiply powers of the same base, add their exponents. Add $1$ and $9$ to get $10$.

288a^{2}b^{7}c^{10}

$288a_{2}b_{7}c_{10}$

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\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

Multiply 2 and 3 to get 6.

6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

Expand \left(6ab^{2}\right)^{2}.

6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

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

36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

Calculate 6 to the power of 2 and get 36.

36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}

Expand \left(2bc^{3}\right)^{3}.

36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}

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

36a^{2}b^{4}c\times 8b^{3}c^{9}

Calculate 2 to the power of 3 and get 8.

288a^{2}b^{4}cb^{3}c^{9}

Multiply 36 and 8 to get 288.

288a^{2}b^{7}cc^{9}

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

288a^{2}b^{7}c^{10}

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

Multiply 2 and 3 to get 6.

6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}

Expand \left(6ab^{2}\right)^{2}.

6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

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

36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}

Calculate 6 to the power of 2 and get 36.

36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}

Expand \left(2bc^{3}\right)^{3}.

36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}

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

36a^{2}b^{4}c\times 8b^{3}c^{9}

Calculate 2 to the power of 3 and get 8.

288a^{2}b^{4}cb^{3}c^{9}

Multiply 36 and 8 to get 288.

288a^{2}b^{7}cc^{9}

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

288a^{2}b^{7}c^{10}

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

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