Problem 35 Simplify. \(\left(\frac{5 x^{5... [FREE SOLUTION]

Chapter 2: Problem 35

Simplify. \(\left(\frac{5 x^{5} y^{2}}{z^{4}}\right)^{3}\)

Short Answer

Expert verified

The simplified expression for \(\left(\frac{5 x^{5} y^{2}}{z^{4}}\right)^{3}\) is \(\frac{125 x^{15} y^{6}}{z^{12}}\).

Step by step solution

Recall exponent rules

Recall that when we have an expression in the form \((a\div b)^n\), we can apply the rule \((a\div b)^n = a^n \div b^n\). This means that we can raise both the numerator and denominator inside the parenthesis to the power of the exponent to simplify the expression.

Apply the exponent rule

Applying the exponent rule mentioned in step 1, we get: \[\left(\frac{5 x^{5} y^{2}}{z^{4}}\right)^{3} = (5 x^{5} y^{2})^{3} \div (z^{4})^{3}\]

Distribute the exponent to each term

Now, we need to distribute the exponent 3 to each term and apply the multiplication rule for exponents, \(a^{m \cdot n} = a^{m \times n}\): \[(5 x^{5} y^{2})^{3} = 5^3 \cdot x^{5 \cdot 3} \cdot y^{2 \cdot 3}\]

Calculate exponents

Calculating the exponents: \[= 125 \cdot x^{15} \cdot y^{6}\]

Simplify the denominator

Now, simplify the denominator by calculating the exponent: \[(z^{4})^{3} = z^{4\cdot3}=z^{12}\]

Write the final simplified expression

Lastly, put the simplified numerator and denominator together: \[\frac{125 x^{15} y^{6}}{z^{12}}\] The simplified expression for \(\left(\frac{5 x^{5} y^{2}}{z^{4}}\right)^{3}\) is \(\frac{125 x^{15} y^{6}}{z^{12}}\).

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91影视

Simplify. \(\left(\frac{5 x^{5} y^{2}}{z^{4}}\right)^{3}\)

Short Answer

Step by step solution

Recall exponent rules

Apply the exponent rule

Distribute the exponent to each term

Calculate exponents

Simplify the denominator

Write the final simplified expression

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