36. Q19a
8 Math Nelson / 9.8 / 36. Q19a
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Similar Question 1
<p>Simplify.</p><p><code class='latex inline'>\dfrac{m^{10}}{m^3 \times m^5}</code></p>
Similar Question 2
<p>Simplify.</p><p><code class='latex inline'>(-c^3)^2\times (-2c)^3</code></p>
Similar Question 3
<p>Simplify.</p><p><code class='latex inline'>x^5\times x^3</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Simplify.</p><p><code class='latex inline'>y^8\div y^6</code></p>
<p>Simplify.</p><p><code class='latex inline'>x^5\times x^3</code></p>
<p>Simplify.</p><p><code class='latex inline'>(m^4)^3</code></p>
<p>Compare and contrast the property for raising a power to a power and the property for multiplying powers with the same base.</p>
<p>What is the square-cube law? consider the following sequence of cubes.</p><img src="/qimages/813" /><p> Write a formula to express the area, <code class='latex inline'>A</code>, of one face in terms of the side length, <code class='latex inline'>l</code>.</p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{2g^2h^3\times (-3g^2h^2)^2}{3gh\times 6g^2h^2}</code></p>
<p>Simplify.</p><p><code class='latex inline'>(2m^3n^2)^4\div (-4mn)^2</code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{(y^6)^3}{(y^5)^2}</code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{33x^5y^7\div 11xy^2}{12x^5y^3\div 4x^2y^2}</code></p>
<p>Error Analysis One student simplified <code class='latex inline'>\displaystyle x^{5}+x^{5} </code> to <code class='latex inline'>\displaystyle x^{10} . </code> A second student simplified <code class='latex inline'>\displaystyle x^{5}+x^{5} </code> to <code class='latex inline'>\displaystyle 2 x^{5} </code>. Which student is correct? Explain.</p>
<p>Wind Energy The power generated by a wind turbine depends on the wind speed. The expression <code class='latex inline'>\displaystyle 800 v^{3} </code> gives the power in watts for a certain wind turbine at wind speed <code class='latex inline'>\displaystyle v </code> in meters per second. If the wind speed triples, by what factor does the power generated by the wind turbine increase?</p>
<p>How is the property for raising a quotient to a power similar to the property for raising a product to a power?</p>
<p>Divide. State any restrictions on the variables.</p><p><code class='latex inline'>\displaystyle \frac{7 x}{4 y^{3}} \div \frac{21 x^{3}}{8 y} </code></p>
<p>Simplify.</p><p><code class='latex inline'>\dfrac{m^{10}}{m^3 \times m^5}</code></p>
<p>Evaluate <code class='latex inline'>\frac{3}{a}\div\frac{a}{3}</code> for each value of <code class='latex inline'>a</code>.</p><p><code class='latex inline'>a=6</code></p>
<p>Simplify.</p><p><code class='latex inline'>a^3b\times ab^3</code></p>
<p>Are <code class='latex inline'> 3 x^{-2} </code> and <code class='latex inline'> 3 x^{2} </code> reciprocals? Explain.</p>
<p>a. Open-Ended Write <code class='latex inline'>\displaystyle y^{6} </code> as a product of two powers with the same base in four different ways. Use only positive exponents.</p><p>b. Write <code class='latex inline'>\displaystyle y^{6} </code> as a product of two powers with the same base in four different ways, using negative or zero exponents in each product.</p><p>c. Reasoning How many ways can you write <code class='latex inline'>\displaystyle y^{6} </code> as the product of two powers? Explain your reasoning.</p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle n^{x+2} \div n^{x} </code></p>
<p>Simplify.</p><p><code class='latex inline'>3x^3y^2\times 5x^4y^3</code></p>
<p>Simplify. State any restrictions on the variables. </p><p><code class='latex inline'>\displaystyle \frac{x^2}{2xy}\times \frac{x}{2y^2} \div \frac{(3x)^2}{xy^2}</code></p>
<p>Simplify.</p><p><code class='latex inline'>(-c^3)^2\times (-2c)^3</code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle n^{5 x} \div n^{x} </code></p>
<p>Error Analysis A student incorrectly simplified <code class='latex inline'> \frac{x^{n}}{a^{-n} b^{0}} </code> as shown below. Find and correct the student&#39;s error.</p><p><code class='latex inline'>\displaystyle \frac{x^{n}}{a^{-n} b^{0}}=\frac{a^{n} x^{n}}{b^{0}}=\frac{a^{n} x^{n}}{0} </code> undefined</p>
<p>Simplify.</p><p><code class='latex inline'>a^5b^4 \times a^3b^2</code></p>
<p>Simplify. State any restrictions on the variables.</p><p><code class='latex inline'> \displaystyle \frac{7a}{3} \div \frac{14a^2}{5} </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 5^{x+1} \cdot 5^{1-x} </code></p>
<p>Consider the expression <code class='latex inline'>\dfrac{3x^3y\times 6xy^3}{(-3xy)^2}</code></p><p>a) Substitute x = —1 and y = 2 into the expression. Then, evaluate the expression.</p><p>b) Simplify the original expression using the exponent laws. Then, substitute the given values and evaluate the expression.</p><p>c) Describe the advantages and disadvantages of each method.</p>
<p>Evaluate <code class='latex inline'>\frac{3}{a}\div\frac{a}{3}</code> for each value of <code class='latex inline'>a</code>.</p><p><code class='latex inline'>a=4</code></p>
<p>Simplify.</p><p><code class='latex inline'>(d^2)^4</code></p>
<p>Find each quotient.</p><p><code class='latex inline'>\displaystyle \frac{f^{4} g^{2} h}{x^{2} y} \div f^{3} g </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \frac{\left(\frac{m^{4}}{m^{5}}\right)}{m^{2}} </code></p>
<p>a. Simplify <code class='latex inline'> a^{n} \cdot a^{-n} </code> .</p><p>b. What is the mathematical relationship between <code class='latex inline'> a^{n} </code> and <code class='latex inline'> a^{-n} ? </code> Explain.</p>
<p>Daniel said that <code class='latex inline'>\displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{\bigcirc}{\bigcirc} </code>. Complete the</p><p>missing fraction, and explain your thinking.</p>
<p>Simplify. State any restrictions on the variables. </p><p><code class='latex inline'>\displaystyle \frac{5p}{8pq} \div \frac{3p}{12q}</code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle \left(\frac{x^{n}}{x^{n-2}}\right)^{3} </code></p>
<p>a. Use the property for dividing powers with the same base to write <code class='latex inline'> \frac{a^{0}}{a^{n}} </code> as a power of <code class='latex inline'> a </code> .</p><p>b. Use the definition of a zero exponent to simplify <code class='latex inline'> \frac{a^{0}}{a^{n}} </code> .</p><p>C. Reasoning Explain how your results from parts (a) and (b) justify the definition of a negative exponent.</p>
<p>Simplify.</p><p><code class='latex inline'>c^5d^4\div cd</code></p>
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