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Anit [1.1K]
3 years ago
14

(A) simplify 3x^-2 (B) simplify 5x^2y(2x^4y^-3)

Mathematics
2 answers:
Black_prince [1.1K]3 years ago
7 0

Answer:

A. \frac{3}{x^2}

B. \frac{10x^6}{y^2}

Step-by-step explanation:

A.

Our expression is: 3x^{-2}, where we have a negative exponent.

Remember that negative exponents are the same as taking the reciprocal of the number and taking that to the positive exponent.

Here, we have x^{-2}, so its reciprocal is just 1/x. Now, we take the positive square of the reciprocal: \frac{1}{x^2}. Put the 3 in and our final answer is: \frac{3}{x^2}.

B.

Our expression is: 5x^2y(2x^4y^{-3}). Basically, we're multiplying these together.

Remember that when multiplying numbers with the same base, we always add the exponents. Here, we have:

5x^2y(2x^4y^{-3})=5*2*x^2y*x^4y^{-3}=10x^2y*x^4y^{-3}

The two x terms will combine to become x^{2+4}=x^6, and the two y terms will combine to become y^{1+(-3)}=y^{-2}=\frac{1}{y^2}.

The final answer is: \frac{10x^6}{y^2}.

Zielflug [23.3K]3 years ago
5 0
<h3>I’ll teach you solve 3x^-2 and 5x^2y(2x^4y^-3)</h3>

——————————————

(A)

3x^-2

Apply exponent rule:

3*1/x^2

Multiply fractions:

1*3/x^2

Multiply the numbers:

1*3= 3

3/x^2

Your Answer Is \frac{3}{x^{2} }

(B)

5x^2y(2x^4 y^-3)

Apply exponent rule:

5y*2x^2+4 y^-3

Add the numbers:

2+4= 6

5y*2x^6 y^-3

Apply exponent rule:

5*2x^6 y^1-3

Subtract the numbers:

1-3= -2

5*2x^6 y^-2

Apply exponent rule:

5*2* 1/y^2 x^6

Multiply fractions:

1*5*2x^6/y^2

Multiply the numbers:

1*5*2= 10

10x^6/y^2

Your Answer Is \frac{10x^{6} }{y^{2} }

Plz mark me as brainliest if this helped :)

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<h3>Answer: Choice A</h3>

x^2\left(\sqrt[4]{x^2}\right)

=====================================================

Explanation:

The fourth root of x is the same as x^(1/4)

I.e,

\sqrt[4]{x} = x^{1/4}

The same applies to x^10 as well

\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4}

Multiply the exponents 10 and 1/4 to get 10/4

\sqrt[4]{x^{10}} = \left(x^{10}\right)^{1/4} = x^{10*1/4} = x^{10/4}

\sqrt[4]{x^{10}} = x^{10/4}

-----------------------

If we have an expression in the form x^(m/n), with m > n, then we can simplify it into an equivalent form as shown below

x^{m/n} = x^a\sqrt[n]{x^b}

The 'a' and 'b' are found through dividing m/n

m/n = a remainder b

'a' is the quotient, b is the remainder

-----------------------

The general formula can easily be confusing, so let's replace m and n with the proper numbers. In this case, m = 10 and n = 4

m/n = 10/4 = 2 remainder 2

We have a = 2 and b = 2

So

x^{m/n} = x^a\sqrt[n]{x^b}

turns into

x^{10/4} = x^2\sqrt[4]{x^2}

which means

\sqrt[4]{x^{10}} = {x^2} \sqrt[4]{x^2}

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