Solve (2a*3b^2)^2*c*(2bc^3)^3 | Microsoft Math Solver

Evaluate

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

Solution Steps

(2 a \cdot 3 b^{2})^{2} \cdot c \cdot (2 b c^{3})^{3}

Multiply

2

and

3

to get

6

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

Expand

(6 a b^{2})^{2}

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

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 (2 b c^{3})^{3}

Calculate

6

to the power of

2

and get

36

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

Expand

(2 b c^{3})^{3}

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

To raise a power to another power, multiply the exponents. Multiply

3

and

3

to get

9

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

Calculate

2

to the power of

3

and get

8

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

Multiply

36

and

8

to get

288

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

To multiply powers of the same base, add their exponents. Add

4

and

3

to get

7

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

To multiply powers of the same base, add their exponents. Add

1

and

9

to get

10

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

Expand

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

Solution Steps

(2 a \cdot 3 b^{2})^{2} \cdot c \cdot (2 b c^{3})^{3}

Multiply

2

and

3

to get

6

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

Expand

(6 a b^{2})^{2}

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

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 (2 b c^{3})^{3}

Calculate

6

to the power of

2

and get

36

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

Expand

(2 b c^{3})^{3}

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

To raise a power to another power, multiply the exponents. Multiply

3

and

3

to get

9

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

Calculate

2

to the power of

3

and get

8

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

Multiply

36

and

8

to get

288

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

To multiply powers of the same base, add their exponents. Add

4

and

3

to get

7

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

To multiply powers of the same base, add their exponents. Add

1

and

9

to get

10

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

Quiz

Algebra

5 problems similar to:

(2 a \cdot 3 b^{2})^{2} \cdot c \cdot (2 b c^{3})^{3}

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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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