Chapter 7: Q24. (page 460)

Simplify the given expression. Assume that no denominator equals zero.
$\frac{- 15 x^{7} y^{8} z^{4}}{- 45 x^{3} y^{5} z^{3}}$

Short Answer

Expert verified

The final expression is $\frac{x^{4} y^{3} z}{3}$ .

Step by step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define quotient of power rule.

The quotient of power rule is given by

$\frac{a^{m}}{a^{n}} = a^{m - n}$

Where, $a$ is any non-zero real number.

Step 3. Simplify the expression −15x7y8z4−45x3y5z3.

Use the property of quotient of power rule.

$\frac{- 15 x^{7} y^{8} z^{4}}{- 45 x^{3} y^{5} z^{3}} = (\frac{- 15}{- 45}) (\frac{x^{7}}{x^{3}}) (\frac{y^{8}}{y^{5}}) (\frac{z^{4}}{z^{3}}) = (\frac{1}{3}) (x^{7 - 3}) (y^{8 - 5}) (z^{4 - 3}) = (\frac{1}{3}) (x^{4}) (y^{3}) (z^{1}) = \frac{x^{4} y^{3} z}{3}$

Hence, $\frac{- 15 x^{7} y^{8} z^{4}}{- 45 x^{3} y^{5} z^{3}} = \frac{x^{4} y^{3} z}{3}$

Therefore the final expression is $\frac{x^{4} y^{3} z}{3}$ .

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Simplify the given expression. Assume that no denominator equals zero.
$\frac{- 15 x^{7} y^{8} z^{4}}{- 45 x^{3} y^{5} z^{3}}$

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define quotient of power rule.

Step 3. Simplify the expression −15x7y8z4−45x3y5z3.

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Simplify the given expression. Assume that no denominator equals zero.−15x7y8z4−45x3y5z3

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define quotient of power rule.

Step 3. Simplify the expression −15x7y8z4−45x3y5z3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Calculus

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify the given expression. Assume that no denominator equals zero.
$\frac{- 15 x^{7} y^{8} z^{4}}{- 45 x^{3} y^{5} z^{3}}$