Solve n^4*2n^2*n^5 | Microsoft Math Solver

Evaluate

2 n^{11}

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Solution Steps

n^{4} \cdot 2 n^{2} \cdot n^{5}

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

4

and

2

to get

6

.

n^{6} \times 2 n^{5}

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

6

and

5

to get

11

.

n^{11} \times 2

Differentiate w.r.t. n

22 n^{10}

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Steps Using Definition of a Derivative

n^{4} \cdot 2 n^{2} \cdot n^{5}

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

4

and

2

to get

6

.

\frac{d}{d n} (n^{6} \times 2 n^{5})

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

6

and

5

to get

11

.

\frac{d}{d n} (n^{11} \times 2)

The derivative of

a x^{n}

is

n a x^{n - 1}

.

11 \times 2 n^{11 - 1}

Multiply

11

times

2

.

22 n^{11 - 1}

Subtract

1

from

11

.

22 n^{10}

Quiz

5 problems similar to:

n^{4} \cdot 2 n^{2} \cdot n^{5}

Similar Problems from Web Search

How do you simplify

n^{4} \cdot n^{3} \cdot n^{2}

https://socratic.org/questions/how-do-you-simplify-n-4-n-3-n-2

Massimiliano Jun 14, 2015

n^{4 + 3 + 2} = n^{9}

How do you use laws of exponents to simplify

2^{4} \cdot 2^{3} \cdot 2^{5}

https://socratic.org/questions/how-do-you-use-laws-of-exponents-to-simplify-2-4-2-3-2-5

2^{12} = 4096

Explanation: Remember that you have:

y^{a} \cdot y^{b} = y^{a + b}

for example if you have:

2^{2} \cdot 2^{3} = 2^{2 + 3} = 2^{5} = 32

How do you simplify

u^{2} \cdot u \cdot u^{- 6}

https://socratic.org/questions/how-do-you-simplify-u-2-u-u-6

See a solution process below: Explanation: First, use this rule of exponents to rewrite the middle

u

a = a^{1}

u^{2} \cdot u \cdot u^{- 6} \Rightarrow u^{2} \cdot u^{1} \cdot u^{- 6}

2 m^{- 1} n^{2} \cdot 3 n^{- 4}

https://socratic.org/questions/what-is-2m-1n-2-3n-4

\frac{6}{m n ^{2}}

\frac{2}{m} \times \frac{3 n ^{2}}{n ^{4}}

\frac{n ^{2}}{n ^{4}} = \frac{n ^{2} ^{1}}{n ^{2} \times n ^{2}} = \frac{1}{n ^{2}}

How do you multiply

3 r^{3} \cdot 2 r^{2} \cdot 3 r

https://socratic.org/questions/how-do-you-multiply-3r-3-cdot-2r-2-cdot-3r

See the solution process below: Explanation: First, rewrite this expression as:

(3 \cdot 2 \cdot 3) (r^{3} \cdot r^{2} \cdot r) = 18 (r^{3} \cdot r^{2} \cdot r)

How do you evaluate

2^{4} \cdot 2^{6} \cdot (2^{3})^{3}

https://socratic.org/questions/how-do-you-evaluate-2-4-cdot-2-6-cdot-2-3-3

2^{19}

Explanation: Let's first look at

(2^{3})^{3}

. We can use the rule:

(x^{a})^{b} = x^{a b}

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n^{6}\times 2n^{5}

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

n^{11}\times 2

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

\frac{\mathrm{d}}{\mathrm{d}n}(n^{6}\times 2n^{5})

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

\frac{\mathrm{d}}{\mathrm{d}n}(n^{11}\times 2)

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

11\times 2n^{11-1}

The derivative of ax^{n} is nax^{n-1}.

22n^{11-1}

Multiply 11 times 2.

22n^{10}

Subtract 1 from 11.

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\frac{x ^{3} y ^{5}}{3 x} \times \frac{y ^{4}}{x ^{2}}

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