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3 years ago

Simplify the expression x^-4×y^3×x^4×y^2.

1 answer:

4 0

For simplifying an expression like this where the same bases with different exponents are to be multiplied, remember the Product rule. It says that when multiplying two or more powers having the same base (x and y in this case), you must add the exponents. For example, here in this expression there are two x's and two y's with different powers so you can simple add the powers of x and for y like shown below:

x^-4×y^3×x^4×y^2

= x^(-4+4) × y^(3+2)

=x^1 × y^5

since x^1 = x so we can omit the power 1 and write x instead.

xy^5 (here the power 5 only raises y and not x since it is not applied to whole)

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What is the solution to the system of equations?

Karolina [17]

Answer: (1,3) or x = 1 and y = 3

Step-by-step explanation:

The solution is the intersection thus the answer is (1,3) or x = 1 and y = 3

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1 year ago

COMPUTE 3 ( 2 1/2 - 1 ) + 3/10

Juli2301 [7.4K]

Answer:

<h3> $\boxed{ \frac{24}{5} }$ </h3>

Step-by-step explanation:

$\mathsf{3(2 \frac{1}{2} - 1) + \frac{3}{10} }$

Convert mixed number to improper fraction

$\mathrm{3( \frac{5}{2} - 1) + \frac{3}{10} }$

Calculate the difference

⇒ $\mathrm{3( \frac{5 \times 1}{2 \times 1} - \frac{1 \times 2}{1 \times 2} }) + \frac{3}{10}$

⇒ $\mathrm{ 3 \times( \frac{5}{2} - \frac{2}{2}) } + \frac{3}{10}$

⇒ $\mathrm{3 \times ( \frac{5 - 2}{2} ) + \frac{3}{10} }$

⇒ $\mathrm{3 \times \frac{3}{2} + \frac{3}{10} }$

Calculate the product

⇒ $\mathrm{ \frac{3 \times 3}{1 \times 2} + \frac{3}{10} }$

⇒ $\mathrm{ \frac{9}{2} + \frac{3}{10}}$

Add the fractions

⇒ $\mathsf{ \frac{9 \times 5}{2 \times 5} + \frac{3 \times 1}{10 \times 1} }$

⇒ $\mathrm{ \frac{45}{10} + \frac{3}{10} }$

⇒ $\mathrm{ \frac{45 + 3}{10 } }$

⇒ $\mathrm{ \frac{48}{10} }$

Reduce the numerator and denominator by 2

⇒ $\mathrm{ \frac{24}{5} }$

Further more explanation:

Addition and Subtraction of like fractions

While performing the addition and subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.

For example :

Add : $\mathsf{ \frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5} } = \frac{4}{5}$

Subtract : $\mathsf{ \frac{5}{7} - \frac{4}{7} = \frac{5 - 4}{7} = \frac{3}{7} }$

So, sum of like fractions : $\mathsf{ = \frac{sum \: of \: their \: number}{common \: denominator} }$

Difference of like fractions : $\mathsf{ \frac{difference \: of \: their \: numerator}{common \: denominator} }$

Addition and subtraction of unlike fractions

While performing the addition and subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fractions. Thus, obtained fractions should be reduced into lowest terms if there are any common on numerator and denominator.

For example:

$\mathsf{add \: \frac{1}{2} \: and \: \frac{1}{3} }$

L.C.M of 2 and 3 = 6

So, ⇒ $\mathsf{ \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} }$

⇒ $\mathsf{ \frac{3}{6} + \frac{2}{6} }$

⇒ $\frac{5}{6}$

Multiplication of fractions

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

When any number or fraction is divided by a fraction, we multiply the dividend by reciprocal of the divisor. Let's consider a multiplication of a whole number by a fraction:

$\mathsf{4 \times \frac{3}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6}$

Multiplication for $\mathsf{ \frac{6}{5} \: and \: \frac{25}{3} }$ is done by the similar process

$\mathsf{ = \frac{6}{5} \times \frac{25}{3} = 2 \times 5 \times 10}$

Hope I helped!

Best regards!

5 0

2 years ago

Find the measure of x.

Andru [333]

Answer:

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent

x is the angle between line with 3 strokes and 2 strokes

The corresponding angle is therefore ∠ C

∠ C = 180° - (63 + 29)° = 180° - 92° = 88°

Then x = 88 → C

5 0

2 years ago

Solve the equation A = bh for b

____ [38]

Hey and thanks for giving me the chance to serve u

8 0

2 years ago

Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of

Annette [7]

If Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of nickels then 0.15 Nickels does Lianne has.

<h3>What is Equation?</h3>

Two or more expressions with an Equal sign is called as Equation.

Given,

Lianne has some dimes and nickels with a total value of $4.60.

The number of dimes she has is 4 more than 3 times the number of nickels.

We need to find number of nickels

From the given information

N+D=4.60

D=3N+4

N+3N+4=4.60

4N=4.60-4

4N=0.6

Divide both sides by 4

N=0.15

Hence, 0.15 Nickels does Lianne has.

To learn more on Equation:

brainly.com/question/10413253

#SPJ1

6 0

7 months ago