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Simplify the following:

[tex]\frac{5x^6 y^7}{10x^2 y^4}[/tex]

Sagot :

GinnyAnswer
Sure! Let's simplify the given expression step-by-step:

[tex]\[ \frac{5 x^6 y^7}{10 x^2 y^4} \][/tex]

1. Separate the coefficients from the variables:

The expression can be broken down into three parts: the numerical coefficient, the powers of [tex]\(x\)[/tex], and the powers of [tex]\(y\)[/tex].

[tex]\[ \frac{5}{10} \cdot \frac{x^6}{x^2} \cdot \frac{y^7}{y^4} \][/tex]

2. Simplify the coefficients:

Simplify the fraction [tex]\(\frac{5}{10}\)[/tex]:

[tex]\[ \frac{5}{10} = 0.5 \][/tex]

3. Simplify the powers of [tex]\(x\)[/tex]:

Apply the rule of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:

[tex]\[ \frac{x^6}{x^2} = x^{6-2} = x^4 \][/tex]

4. Simplify the powers of [tex]\(y\)[/tex]:

Similarly, apply the exponent rule:

[tex]\[ \frac{y^7}{y^4} = y^{7-4} = y^3 \][/tex]

5. Combine the simplified parts:

Putting it all together, we get:

[tex]\[ 0.5 \cdot x^4 \cdot y^3 = 0.5 x^4 y^3 \][/tex]

Therefore, the simplified expression is:

[tex]\[ \frac{5 x^6 y^7}{10 x^2 y^4} = 0.5 x^4 y^3 \][/tex]
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